I think its a possibility, particularly if FDR doesn't attain the White House, or the Business Plot went off as a backlash against it. But I think you'd more likely have a coalition of left wing groups and popular unrest, union strikes, rioting, etc. and non Communist leftists like Upton Sinclair would be involved. Eventually, the Communist Party would ride the wave to power possibly, but might have to make the pretense of power sharing before doing any purges. I could see some 1930s gangsters siding with the Revolution for power like Dillinger, who had somewhat leftist views. I could also see union bosses like Harry Bridges who was a communist but an immigrant from Australia who was a labor leader in San Francisco becoming powerful in this scenario.