As mentioned in the first answer, the Italians were parts of an important theater: the Mediterranean Sea.

One could argue that wit Italy remaining neutral, the Germans would have stayed out of the Mediterranean theater. But the consequences would have been huge:

With the neutrality of Italy, the Allies could use the sea as a short line of communications to Egypt (and thus India and Australia). The navy in mediterranean would have been only of a little help to the Atlantic battle, because frigates were more necesary than cruisers, destroyers or battleships. However these boats would have been an help to oppose the Japanese Navy.

The second point is that the South of France "free zone", would have been close to the English forces: thus, it is likely that the "Free zone" of Vichy would have not existed and that the Maghreb, along both Syria and Lebanon would have fight to prepare a landing on the South Coast of France. Somehow, the Germans would have entered a battle for the Mediterranean Sea, but not with the good strategic position of the Italian territory.

So no, the Allies did not benefit of having the Italy enter the war on the side of Germany rather than remaining neutral.

Italy won just one major battle without Germany's help: the conquest of Somaliland.

Everywhere else, the Italians were beaten by the British... and sometimes even without British help. The Greek forces pushed them back into Albania, they were fought to a standstill in Yugoslavia.

The British forces defeated them in North Africa. In every case, this created a humongous risk for the Germans, who couldn't afford to let the British get a toehold on the continent. So the Germans, expending personnel and materiel, had to bail out the Italians every time.

So yes, the Italians inadvertently helped the Allies.

All things considered and with perfect hindsight, did the Allies benefit, by having Italy fight on Germany's side rather than remain neutral?

No.

While the popular impression is that Germany had to "bail out" Italy more often than not, this does not mean they were a net burden on the Axis. On the contrary, Italy opened up the Mediterranean and African theaters of war that required an extensive diversion of resources, ships, aircraft, men, and material to fight in the very critical early years of the war. The campaign to clear the Mediterranean and then liberate Italy went on through the whole war. All that could have been instead fighting Germany.

Hostile Italians also prevented the Allies from using the Mediterranean as a "British lake". The Italians threatened the supply lines between Britain and her Empire, Allied supply lines to the Pacific and the Soviet Union. They prevented the Allies from using the Mediterranean to stage raids and attacks on Southern and Central Europe.

To avoid a "what if" answer that's frowned upon here, I'll instead go into the ways the Italians tied down Allied forces and delayed Allied victory.

The Regia Marina and Aeronautica

The Regia Marina and Regia Aeronautica (Italian Royal Navy and Air Force) during WWII were a large, modern, and powerful threat, if not the best commanded, that required a diversion of large numbers of British ships, aircraft, and men to fight. This stretched the British even thinner than they already were.

Germany alone had no hope of combating the Royal Navy on the surface, but entry of Italy gave the Axis something closer to parity. The battles in the Mediterranean pulled away aircraft and anti-air artillery desperately needed for the Battle of Britain. They pulled ships away from the Battle of the Atlantic. The British Army was unable to defend Greece because they were busy fighting the Italians in North Africa and had to halt their successful offensive there to transfer troops to Greece ultimately suffering in both theaters. 100,000 British colonial troops were tied down fighting the Italians in East Africa.

It was during this critical stage of the war, 1940 to 1942, that Germany could have won. During this period the Italians were effective at tying down British resources.

The Italians also made it difficult for the British to use the Mediterranean as a British lake. It secured the German southern front against air attack and invasion. Without the Italians in the war, Britain's Mediterranean holdings could be used as a staging area for an invasion of Southern France or bombing German submarine pens in Western France.

Naval Historiographer Drachinifel and Military History Visualized did a piece on Italy's forgotten WW2 Victories? which expands on the impact of a hostile Mediterranean and the effect on the Pacific War and convoy battles.

In particular he points out…

• The fast transports and escorts used in the defense and resupply of Malta.
• The heavy units needed to counter the Italian Navy.
• The 135 British ships lost in the Mediterranean.

Mers-el-Kébir

One of the most infamous actions by the British during the war was their attack on the powerful Vichy French fleet at Mers-el-Kébir in North Africa. After the fall of France the British feared the French fleet would be seized by the Axis and allow them to stretch the Royal Navy even thinner than it already was, so they destroyed them in harbor. This severely strained Anglo-French relations and could have tipped Vichy France into declaring war on the British; what one normally does after you attack their navy.

It might not have happened with a neutral Italy.

While the Kriegsmarine gets all the attention, particularly Bismarck and Tirpitz, the German Navy was quite weak. Even combined with captured French ships they could not seriously challenge the Royal Navy. But the Kriegsmarine, the French Navy, and the Italian Navy was a very serious concern. With major French naval warships anchored in North Africa, their being seized by Italian troops from Libya was a real concern.

North African Theater

The entire North African theater from mid 1940 to mid 1943 is because of the Italians. The German Africa Corps gets all the press, but the only reason they were in North Africa at all was to bolster the Italians.

The popular narrative is that the Germans had to rescue the Italians from defeat, and there is truth in that, but the bulk of Rommel's army was Italian. North Africa was a side-show for the Germans compared to what they were sending to the Eastern Front and using to garrison their empire. At Second El Alamein, the height of Rommel's advance, Panzer Armee Afrika was just three divisions while the Italians had eleven.

From the see-saw battles across Egypt and Libya in the east, to the massive US and British landings of Operation Torch in the west, to the final battles in Tunisia. Hundreds of thousands of Allied casualties, multiple amphibious invasions, thousands of tanks and aircraft and vehicles lost, dozens of ships, hundreds of transports... all because Italy was in the war.

North Africa and Italy get invaded, not Norway or Greece

When the Western Allies were planning their second front in 1942, and after ruling out the fantasy of invading Europe, several options were considered. The Allies chose Italy, but Italy was only one option.

An invasion of Norway was very tempting to the Allies: cut off the iron ore supply to Germany, prevent its use to threaten northern supply lines to the Soviets, open a new supply line to the Soviets, place Allied aircraft within easy reach of Germany.

An invasion of the Balkans was also considered. Liberate Greece, link up with partisans in Yugoslavia, threaten Romanian oil fields, open a new supply line to the Soviets.

The Allies had to invade somewhere to take pressure off the Soviets. With Italy neutral, the Allies would have chosen another location to invade. In Italy, the Allies had to fight the Italians and the Germans. Without Italy, this invasion would have to be defended with solely German troops stretching the Wehrmacht even thinner.

Finishing off Italy

When the war in Europe ended, fighting was still going on in Italy drawing away Allied resources.

Finishing off the Mediterranean theater required a huge invasion by both US and British forces. Operation Torch, Tunisia, and Sicily involved 500,000 troops and much of the Allied naval transport capacity fighting mostly Italians. While the Americans advocated invading France in 1943, the decision to invade Italy probably delayed the invasion of Europe by a year.

Even after the Italian Armistice, the march up the Italian peninsula remained a very costly distraction for the Allies. It's questionable what the end goal was. Germany could fight the Allies in strong defensive terrain and ultimately fall back to the defensive line of the Alps.

Without Italy in the war there would be no Mediterranean nor African nor Italian fronts to draw British resources away from Germany in the critical early years of the war, nor would there be an Italian liberation campaign to delay the invasion of Europe.

Supplying the British Empire and the Pacific War

In addition to the direct effects, the Italians made the Mediterranean dangerous for use as a supply line to the Pacific and the Soviet Union.

After 1941, Allied ships wishing to reach the Pacific Theater quickly could avoid having to go around Africa by using the Suez Canal. Similarly, the Allies had a supply line to the Soviet Union, the Persian Corridor.

With Italy in the war this presented a terrible choice: run a gauntlet of Italian ships and aircraft in the Mediterranean in the hopes of getting there faster, or go all the way around Africa adding weeks to the journey and making themselves vulnerable to German U-Boats and surface raiders. Both required additional escorts. Both added risk and time to supplying these theaters.

These supply lines made it vital that the Italian navy and air force were dealt with drawing yet more forces away from fighting Germany and delaying supplies to the Pacific and Soviet Union.

Italy contributes to Japan's success

Italy being in the war had a profound effect on the Pacific War. I picked up on this from Drachinifel's Drydock #43.

As above, a belligerent Italy drew away a significant portion of the British armed forces to defend their interests around the Mediterranean. This, in turn, left Britain's Pacific holdings thinly defended. Britain's plan was to essentially bluff. If attacked they would abandon their outlying holdings and fallback to Singapore, India, and Burma. Few reinforcements would be coming until the Mediterranean was under control.

The capture of the SS Automedon in Nov 1940, and her top secret documents outlining all this, gave the Japanese assurance that the British were a paper tiger. Emboldened by this information, the Japanese knew they could send the cream of their Navy on far-flung offensives without being concerned with a major British counter-offensive.

If, instead, the Italians were neutral this would have freed up significant assets to reinforce the British Far East, and allowed the British to take a more active and offensive attitude towards Japan.