It's an interesting coincidence, but I don't think anybody called Stalin "Uncle Joe" until the 1940s. Here is a quote from Anthony Beevor (2002) in Google Books preview:
Roosevelt, hoping to lighten the atmosphere, told Stalin that he was popularly known as 'Uncle Joe'. Stalin, who had clearly never been informed of this by his own diplomats, was insulted by what he regarded as vulgar and disrespectful nickname.
FDR himself had popularized the nickname to get Americans behind the somewhat unsavory ally the USSR had become in 1942.
But Beevor missed something. Already in 1949 Edward Reilly Stettinius, Jr., in Roosevelt and the Russians
(pg. 115), had the story this way:
When Stalin appeared to be offended, Molotov told us not to be deceived. "He is just pulling your leg," Molotov told us. We have known this for two years. All of Russia knows that you call him 'Uncle Joe.'"
How socialism was portrayed in film during the Great Depression I'm not too clear on, but I think it may have peaked early in the Depression. Overseas, Metropolis
(1927) had already come out before the Depression, with the boss's daughter on the workers' side!
If you believe in guilt by association, it does seem the Soviets appreciated this film more than the Americans. In 1936, a list of only three foreign films were allowed to be shown in the USSR, and it was one of them. A leftist French film was rejected because the workers were too well dressed. (Cinema and Soviet society, 1917-1953
, by Peter Kenez, p.134, another adventure in Google Books.)
More to the point, Curtiz and Warner Bros. were the home of the "social problem film," and, roughly, the Democratic Party, as opposed to MGM & the Republicans. (Friend or foe? Russians in American film and foreign policy, 1933-1991
by Michael J. Strad and Harold R. Trope, p.20.) The prologue titles to the film carefully lay out the center line the film will take on actual politics. By 1932 the Democratic Party was facing strong, potentially explosive, pressure from the left. Huey Long helped get FDR nominated in '32 but was then sidelined, and assassination stopped his plans to oppose, or help oppose, FDR in the 1936 race.
The film's clearly a bit optimistic about the political process in a cotton town. But it's interesting the speaker invokes "the governor" in his speech at the end. Apparently Huey Long or someone like him was a big fright to the planters.