It's actually a good question but I will say that I have 2 main systems one with a 5900x and one with an 8700k @ 5.0 ghz (delided). I also have an RTX 3080ti as well as a 6650xt. I have swapped out the GPU's in both for testing regularly and I typically game at 1440p (I have high refresh rate 1440p and 1080p displays). At 1080p the 5900x does make a difference with the RTX 3080ti -about a 15-20% FPS gain sometimes 30%. AT 1440p the 8700k is within 5-10%. With the 6650xt - the 6650xt being in between an RTX 3060 and RTX 3060ti level of performance and there is little gain to be had FPS-wise with either processor regardless of the resolution.
So my take on this is that if you play or plan to play at 2k res high refresh rate which is really what the RTX 3080ti is best at I would look at something like a 12600k/12700k/5800x/5900x eventually to get that extra 5-10% performance but you could also wait since the FPS difference is somewhat small at that resolution. If you want to save some money keep a 5 ghz OC on the 8700k and wait for Intel 13th Gen and AM5 to drop. On the other hand if you play at 1080p high refresh yes a processor upgrade will benefit you now.