Was Stalin behind the idea of universal elections in the USSR?

Revolution in a backward country
It is true that in many ways Stalin reverted to the "old capitalist ways". However, there is a deeply communist rationale for such policies, which have nothing to do with the desire to establish a western style liberal democracy.

The problem lies in the fact that Marx and collaborators developed their theories for a developed capitalist country, such as were at the time France, Britain, the United States and to some extent Germany. In the logic of historical materialism: all these countries had already experienced the bourgeois revolution (i.e., transition from a feudal system to the capitalist mode of production), characterized politically by the establishment of a parliamentary liberal democracy and universal suffrage. Communist/Socialist revolutions were expected to take place in these countries, because (among other things):

• the proletariat formed the majority of the population in these countries
• the existing capitalist production relations were sufficiently developed (in Marx' opinion) to provide for the whole population, after the nationalization of industry (i.e., to implement the famous principle "From each according to his ability, to each according to his needs".)

Russia did not satisfy these conditions - the majority of its population were peasants, who wanted to have land as their personal property, its industry was poorly developed, and its proletariat was small and lacked sufficient consciousness for transitioning to the Communism. Thus, Russia needed to go through the development of Capitalism, just as the western countries did in the XIX-th century. Marx did allow for the possibility that Russia transition direct to Communism, but only under the condition that there is simultaneous Socialist revolution in Europe.

That the Communist takeover in Russia would be accompanied by a Europe-wide revolution was indeed the expectation, seen as a precondition for the survival of the Communist regime in Russia. When this didn't happen, they indeed had to modify the theory, but introducing a concept of the Communism in a single country, and rolling back many of the sweeping communist reforms adopted in the early years after the revolution.

Since the Russian Communist didn't intend to give up their power, the transition to the Communism was supposed to pass through a prolonged period of the Dictatorship of the proletariat (Marx and Engels had postulated that such a period might be necessary, but they never spelled how long it could take). During this period the proletariat gradually develops the capacity to manage large-scale industry, while destroying the capitalist way of life.

The New Economic Policy was an even more explicit (although abortive) attempt to rush Russia through the capitalist stage of development. This problem was dealt with on a much large scale and in a longer period of time in China - even more agricultural country than Russia at the moment of revolution. In China, likewise, various attempts for quick transformation to Communism had failed (Great Leap Forward, Cultural Revolution, etc.), so that it eventually reverted to Capitalist society, although under the guidance of the Communist Party and in the conditions of supposedly non-antagonistic coexistence of classes.

A good reference here is Marxism after Marx by David McLellan.

Council system vs. Parliamentary democracy
Marxism opposes western-style parliamentary democracy, as a system which guarantees nominal, but not real equality. Indeed, people more privileged by birth, education, intelligence, physical strength or beauty, communication skills and other characteristics necessarily get bigger share of the pie in a liberal democracy, despite the seeming equality of rights. What is seen as main problems are:

• the parliament (or elected government) is not representative of the real producers of the value (value as viewed by Marx, but not by the mainstream western economists)
• once elected, the elected representatives are not responsible to the voters until the next election, and therefore subject to corruption (i.e., becoming tools of the capitalist class in exchange for material favors or help in getting re-elected.)

Marxist alternative is the Council system (Soviet is just the Russian word meaning Council.) Councils are formed at workplace, and exist on different levels - with representatives of lower councils elected to serve at higher levels. The council can recall their representative at any time - which is supposed to remedy the problem of corruption.

Introducing the council system was one of the key elements in Russian Communists trying to rush in the advent of Communism. It also had a convenient side effect of giving legitimacy to the claim that the elected National Assembly has been superseded by a more democratic system, and thus dismissing the Assembly (where the Bolsheviks didn't have majority.) Kautsky covers this in many details in his Dictatorship of the Proletariat, pointing also the arbitrariness of inclusion and exclusion from councils. Lenin's response The Proletarian revolution and the Renegade Kautsky mainly disputes whether Kautsky's view really represents Marx, although acknowledging the basic facts (Lenin's attempts to justify the Bolshevik measures as greater level of freedom and justice seem obsolete in historical perspective.) Finally, the council system as a form of "government" was apparently developed in details by Gramsci in his Prison notebooks.

Thus, return to the elections based on territorial principle constituted a reversal of a major Communist achievement. On the other hand, preserving the right of recall was supposed to soften the magnitude of the reversal (However, it is not clear whether this recall could be immediate, as in the council system, or via new elections, as, e.g., often practiced in the US.)

Disclaimer:
If any phrasing above appears too sympathetic to the Communist case, it is purely accidental. My only goal here is to provide a more informed opinion on the subject.