No, if you really look at the things that killed the American left, fear of the Soviets doesn't really become a factor until after WW2, and that's because of the end of isolationism, America taking a commanding role on the world stage, and most importantly, the existence of atomic weapons.
There were many things that conspired together to kill the American left. But the mere existence of a self-proclaimed revolutionary socialist state half a world a way didn't really figure. The First Red Scare was entirely about domestic subversives, and was more focused on the cliche of the bomb throwing anarchist than Bolshevik fifth columns. What hurt the American left was an inability to overcome tension between immigrant and native born workers, the ever present race issue, the battle between reformists and revolutionists being the most fratricidal of any nation, the poor timing of the First World War, which hit during a very critical development phase in the movement, and the immense level of violence by both the state and private actors against leftists.
