When planning Barbarossa, did Germany conceive of the Soviet migration of heavy industry?

Certainly no. They planned to finish the war in 1941, there is a lot of indication of this. One crucial piece of evidence is that they did not equip the troops for winter. Of course it was not possible to move the industry before the end of 1941, and even what the Soviets performed was a great surprise for everybody.

That's a definite no. German intelligence about the Soviet Union was abysmal. Not just bad, but abysmal. They estimated the number of Soviet military units wrong by well over 1000%. Not only that, they assumed less than half of what they assumed could be armed. Nearly all units were armed.

The Germans didn't know about the T-34 before they met them in battle. They could have known about the KV-1 heavy tank (Winter war) but that one came a surprise. The German air force was tactical, and lacked heavy bombers. Even if they wanted to, they weren't able to reach the Ural or beyond.

I never understood why the Germans with all the above disadvantages even bothered to try.

• https://www.youtube.com/watch?v=ft-dYaZKxwU
• https://www.youtube.com/watch?v=A_3R-Rkn_98

Indeed, the Germans rested their planning on the almost outlandish ideas of ideology, resulting overconfident optimism and not on facts they knew, ought to know or could have known. Concerning industry, capability, manpower and organisation, all estimates were way off the mark. The Germans charged General Thomas with the economic planning of the to be expected consequences of Operation Barbarossa.

The second study called for by Hitler proposed answers of an economic kind which General Thomas as head of the War Economy and Armaments Department was charged to answer.[…]
Thomas thus delivered a report lavish in discussion of the long-term economic benefits to be derived from occupying the Soviet Union and entirely dismissive of contradictory evidence previously produced as well as the dubious nature of his source material. Furthermore, his study ignored questions relating to the military feasibility of achieving the distant economic goals even though they required the conquest of an enormous land mass. Specifically, Thomas emphasised the need for the rapid conquest of the Caucasus for oil and a connection to the Far East to ensure future rubber supplies. Grain was expected to flow from the Ukraine solving Germany’s food shortage and 75 per cent of the Soviet armaments industry was to fall, it was hoped intact, under direct German control with the remainder posing little threat so long as the factories in the Urals were destroyed. (p85–86)

This matches quite well the German experience early on of recording a number of completely destroyed enemy divisions that exceeded the estimated total number number of divisions available to the Soviets by quite a margin…

But these were just those voices that were listened to. One of the most recognised commanders of the war had differing opinions way before the war:

Describing the Soviet state in 1937 Guderian wrote:

Russia possesses the strongest army in the world, numerically and in terms of the modernity of its weapons and equipment. The Russians have the world’s largest air force as well, and they are striving to bring their navy up to the same level. The transport system is still inadequate, but they are working hard in that direction also. Russia has ample raw materials, and a mighty armaments industry has been set up in the depths of that vast empire. The time has passed when the Russians had no instinct for technology; we will have to reckon on the Russians being able to master and build their own machines, and with the fact that such a transformation in the Russians’ fundamental mentality confronts us with the Eastern Question in a form more serious than ever before in history.

To illustrate this correct assumption with numbers:

For reasons of dispersal new production facilities of the heavy and chemical industry were now being increasingly set up also in the eastern parts of the country, in the Urals, central Asia, eastern Siberia, and even the Far East, on the basis of the rich raw-material and energy resources located there. The creation of a second industrial base in the eastern parts of the country was of considerable strategic importance, as these plants would be virtually beyond the reach of a potential enemy. In 1940 the coalmines of Kuznetsk, Karaganda, the Pechora region, near Irkutsk, Chita, and Sangar already accounted for 35 per cent of the total Soviet output of coal and for 25 per cent of coke production. During the same year the iron and steel plants established in the eastern parts of the Soviet Union—at Magnitogorsk, Kuznetsk, Novotagil, Chelyabinsk, and Novosibirsk — were supplying 28 per cent ofthe total output ofiron ore, 28 per cent of pig-iron, 37 per cent ofsteel, and 36 per cent of rolling-mill products. Some 25 per cent of the country’s total energy was generated in the east, as was 12 per cent of crude oil. The importance which this second industrial base had attained by 1940 can further be gauged from the fact that over 50 per cent of the 31,649 tractors manufac­ tured in the Soviet Union and 14 per cent of its 58,437 machine-tools were produced there.

That is of course only a short estimate at the already apparent distribution and diversity of the economic base that would have to be acknowledged, not the remote or even inconceivable idea of relocating that base swiftly on short notice.

But then it has to be said that the scale of the Soviet evacuations were quite simply unheard of before, as well as the scale and grace under pressure of the industrial output on the whole. Even before the ware started at all the Soviet industrial base was superior to the German counterpart. How quickly and comprehensive the evacuation happened under very unfavourable circumstances:

In the face of the unrelenting German advance, the enormous evacuation of Soviet industry to the east in 1941 was indispensable in ensuring the economic durability of the Soviet Union. Accomplished with extraordinary speed and under the most adverse circumstances, which included aerial attacks from the Luftwaffe, hundreds of factories were simply uprooted, transported into the interior and rapidly reassembled. The scale and complexity of such an undertaking is difficult to imagine, especially in the light of the national crisis overtaking the country, yet here post-war Soviet literature’s propensity for grandiose superlatives such as ‘heroic’ and ‘historic’ seem justified.
Between July and November, 1,523 industrial enterprises were moved to the Volga region, Siberia or Central Asia, amounting in total to some 1.5 million railway wagonloads. Even more remarkable, the production of vital war materials actually increased in the second half of 1941, with official production quotes in some cases, such as tanks, being exceeded. Indeed the Soviet Union produced more tanks in 1941 than Germany and 66 per cent of these were of the newer T-34 and KV-1 variety. Soviet industry also turned out more aircraft and a great many more artillery pieces than Germany, helping to meet the most immediate needs of the army.

Nevertheless, the really crucial total data for status quo ante that was available, in principle, was twisted into ignoreance, to please a certain man:

In his deliberately factual exposé General Thomas based himself on the same data as were also used by the Army High Command. The crucial difference was that Thomas in his memorandum created the impression that the economic resources and, more particularly, the armaments industry in the European part of the Soviet Union could be captured intact, and within a short period of time put to the use of the German war effort. In doing so he disregarded the real central problem of the whole operation, i.e. the question whether the Soviet regime would in fact rapidly collapse under the German assault, so that the expenditure of time, personnel, and material on the campaign could be kept within limits. Had Thomas wished to ‘dissuade Hitler from his decision with all means at his disposal' he could easily, with the information available to his department, have confirmed the objections to such an assumption, the objections contained, for instance, in the Walther memorandum. Furthermore, he could have factually refuted Hitler’s expec­tations of rapid and vast economic gain in the cast. He did not do so, and the charge that he was an ‘opportunist and a double-dealer’ was perhaps not unjustified. Whatever objective Thomas may have pursued with his memor­andum, to Hitler it certainly came as a confirmation of his own views.
(From: Horst Boog et al al. (Eds): "Germany and the Second World War. Volume IV. The Attack on the Soviet Union", Oxford University Press: Oxford, New York, 1996.)

Quotes from: David Stahel: "Operation Barbarossa and Germany’s Defeat in the East", Cambridge Military Histories, Cambridge University Press: Cambridge, New York, 2009.

I'm wondering if Hitler or others conceived of this possibility when they were planning Barbarossa?

(Note: much of this is derived from Wikipedia, I don't have the referenced sources.)

It seems they conceived the opposite. They were so confident the Soviet army would be unable to function without their supplies from European Russia that they would stand their ground and fight. The battle would be over before winter in 1941 and the invasion would end at the Urals.

The operational goal of Barbarossa was to reach the Ural Mountains and form a new frontier there, the A-A line from Arkhangelsk to Gorky then following the Volga all the way to Astrakhan on the Caspian Sea. This would cut off most of the Soviet's industrial, food, and oil production, and give a clear geographical defense line. Arkhangelsk was used to supply the Whites during the Russian Civil War after WWI; with it seized no help would be coming from the West. The Caucasus are west of this line cutting off the Soviets from their oil and also supply from the Black Sea. With the Ural Mountains and Volga River forming a geographic defense line, and the Soviet military destroyed and unable to rebuild, they could shift troops to another front, or demobilize them. German colonists would be sent to the Urals form a cultural wall, militia, and supply base for the garrison.

Hitler had no interest in attempting to invade and occupy the trans-Ural Soviet Union. Not only because he was looking to unite Europe, but because he did not consider it a threat. He considered it as likely that Stalin would be able to mount an offensive from there as if he would be able to mount an offensive from Slovakia bereft of all the population and industrial capacity of Germany.

Barbarossa was also conceived as a quick victory before the winter of 1941. It was assumed that once the Soviet army was decisively defeated in the field and their major cities taken, the Soviet Union would either surrender or suffer a popular uprising. Or both. Given that's how Germany's invasions had all gone to date, this was not such an outlandish idea. They were so confident that proper winter clothing and supplies were not prepared.

In addition, the Germans examined Napoleon's defeat after chasing the Russians on a long retreat. They did not think a repeat would happen because a mechanized army needs to be supplied, and their supplies were concentrated west of the Urals. They assumed the Soviets would not be able to fight without the Baltic (trade access with the West), Ukraine (food), Leningrad (industry), Moscow (transport, industry, political heart), and the Caucasus (oil). Thus they would stand their ground and be defeated by the German army, rather than having to be chased across the vast Russian steppes. Their main concern seems to be able how to transport and supply such a large army across such long distances, and how the infantry might keep up with the panzers; just getting sufficient forces to Moscow in time was a huge stretch.

The original Soviet plan conformed to these expectations. They planned to put a third of their army close to the border to dig in and slow or halt an attack. The rest of the army would reinforce and counter-attack to push the invaders back and drive deep into German territory. The goal, as with much of the initial military thinking in WWII, was to fight on someone else's territory and make their people deal with the horrors of war, not your own. This plan ignored the deficient state of the Soviet army to fight a mobile war in 1941. Initially, the Soviets acted according to German expectations.

Finally, what the Soviets accomplished was unprecedented. Entire factories and populations were moved thousands of miles across rugged terrain in wartime and rebuilt. I do not believe this is something any industrial nation would consider possible in 1941, and certainly the condescending Nazi racial and political views of the Soviets would not allow them to think the "racially inferior" Slavs and "industrially backward" Soviets capable of such feats.

The planners of Barbarossa saw no reason to advance beyond the Urals, and that the Soviet army would be unable to be supplied without European Russia. They thought that the campaign would be over before winter 1941. German planning prior to the invasion had more concerns about whether their own transport and logistics would keep up than fighting a prolonged battle with the Soviets. The Soviet feat was unprecedented, and the racial views of the Nazis would not allow them to believe it was possible. No, I believe they had no concept that moving Soviet industry beyond the Urals was even possible.