About an RTX 3080 / 4070 (non super) class GPU is where you would start to see any difference from the 12600k and the new R7 7800X3D or 9800X3D. I think you meant 1440p and that further mitigates FPS leads from a more powerful CPU-GPU combo to a less powerful CPU with the same GPU. So, the answer to your question is that with an RTX 3070 no discernable difference.
Mostly depends on the settings you're using and will vary from game to game. The best way to tell where your gaming bottleneck likely is would be to run an overlay which checks GPU usage and if it's in the 90%+ range your video card is the limiting factor.
Some games you'd likely get a good boost on, but many I'd imagine you would not. I feel confident saying you would get more out of spending that money on a new video card than you would new CPU/mobo (and potentially new memory).