My question is “Can I expect to see at least double the frame rates I currently get?”
With a latest generation AMD / Intel CPU and a 3080 (waiting for the new models is wiser) and depending on the resolution used, we can claim a good framerate between 45/60 FPS in ULTRA setting. This is the case for me, I currently have a 2080 Ti with a 5950x and 32 GB of ram.
It all depends on your budget.
On my old pc with an I7 2600K, 1660 Ti, I was at 25/40 FPS in HIGH setting, if that helps give you an idea.
So no need to spend a lot to have a good end result.