Yes, the Great Depression was enormously advantageous to Soviet propaganda. The Soviet Union was the sole industrial country left largely unaffected [outwardly] by the Depression, affirming the Bolshevik belief in the untenability of modern capitalism and aspiration for worldwide revolution (by the late 1930s this internationalism is lost in favor of Bukharin's 'socialism in one country’).

We can point to several factors helping the USSR: significantly, the Soviet Union, in 1929, did not rely on these international markets in the way that the West did. Internal production had been on the rise in the years preceding the Depression, which actually precipitated growth from Western investors. To import foreign goods yet overcome increased tariffs that were intended to mitigate the economic downtown within those countries, the Soviet Union just exported more. This was possible due to industrial impacts of the Five Year Plan; agriculturally it was carried out, but wasn’t viable (there’s only so much grain, and one of the immediate impacts of collectivization was a decrease in harvest) - this is one cause of many for the famines in Ukraine and Central Asia. But 1929 also marks Stalin’s rise as the singular leader of the Soviet Union; Trotsky was exiled early that year, while Zinoviev had been expelled in 1927 along with Kamenev. Rykov would be ejected from the Politburo the following year. The utopian fantasy of the Bolsheviks gave way to authoritarianism right as the sustainability of capitalism was thrown into question around the world. Russian-language propaganda would affirm the power of the Soviet system over that of the West, direction workers to embrace the kolkhoz and, increasingly, express concern over German and Italian fascism throughout the 1930s. Dovzhenko's Ukraine Trilogy, culminating in Earth (1930), affirms the benefits of collectivization while portraying Kulaks and religion in a remarkably negative light. The Deserter (1933) is not a particularly exceptional film, but it portrays a Communist worker in Germany who is repressed by the police, but embraces the Soviet system when he is sent abroad as a delegate.

This Soviet jubilance is coupled with Western skepticism of capitalism in the face of 30% unemployment. David Kennedy writes of this internal loss of faith in capitalism:

Disillusionment with Roosevelt ran deepest and most dangerously on the left, especially among jobless workers and busters farmers, among reformers and visionaries who had been led to giddy heights of expectation by Roosevelt's aggressive presidential beginning, and among radicals who saw in the Depression the clinching proof that American capitalism was defunct, beyond all hope of salvation or melioration.

The kinship between European, American, and Russian communists and socialists merits its own discussion; though after the Depression, I recommend Andre Gide’s Return from the USSR to see the impression the Soviet Union of the late 1930s leaves (while obscuring the nascent Purges).