Whole world? No. I doubt it.
Russia was devastated by the war on a manpower and production level that took a while to recover; in some ways, it still hasn't really recovered in terms of manpower compared to their former advantage.
But if the US wasn't around, I think Western Europe goes Communist, peacefully for the most part. There would a wide swathe of areas that would be Communist that were not OTL. Franco might get forcefully deposed by the Red Army.