No bottleneck; a 5600X is more than enough foran RTX 3080 at 1440p.
For most games, the bottleneck will be the monitor's refresh rate.
A faster GPU will always perform faster than a slower GPU even on a bottlenecked CPU. Faster CPUs can raise this FPS cap a little more, this is usually seen for running high refresh rates above 240FPS on lower resolutions such as 1080p.
This is because GPU load scales with resolution, but game logic stays the same and runs on CPU. At 1440p your machine will be able to use most of the RTX 3080 graphical capacity.
You can test for yourself: If the FPS increases further when going down to 1080p (say 100 to 160), that means your system is still GPU limited. If the FPS stays about the same whether at 1440p or 1080p (say 300 to 320) means there is probably no bottlenecking.