Maybe
Their goal was to spread communism across the globe. I don’t know if that means the USSR would control it all, or if there would just be a bunch of Communist countries. I do know Stalin said he would bury us. I think he meant it.
Fortunately North America never had to find out.
Here is a thought. What would have happened to communism had the USSR achieved its goal of taking over the world? I suspect they could not have held onto it for long and would be fighting conflicts everywhere.
After a few generations and leaders, they would have probably be where China is, more socialists than communist.