Let's say the Bolsheviks offer him a really good deal in 1918, and that he takes it. (I don't know his personality; was he ideologically opposed to them?) Over the next forty years, he continues to work with them, and they fund his helicopter research. What happens?
He would be likely chained to his work on seaplanes. This was one area of aviation Soviets performed miserably at. They could not build working bigger seaplane pre-WWII IOTL and had to live with licensed designs from (oh horror) Fascist Italy and Nazi Germany, which really
was a source of embarrasment. However, with the way Soviet system worked, he probably could spare a bit of resources and manpower in his R&D facility to work on helicopters on a smaller scale. Therefore I doubt that him staying in USSR would seriously increase the pace of the Soviet heli program (although it will surely delay American progress, as he seemed to raise American heli efforts from non-existence almost single-handedly). Later on (post-1945) he could work on helicopters, but Russians seem to do not so badly without him IOTL, with Mil and Kamov.
And BTW, Nazi had helicopters, they just had no time to develop a concept of usage...