Whether or not the CPU will be a bottlneck greatly depends on a few other factors.
What's the refresh of your monitor, and what quality of in game and driver settings do you like to play with? For example, if you have 244hz monitor, "need" 244 FPS and just play esports games with all the game and driver settings on low, then you'll need a fairly fast CPU.
In this case Ryzen 2600x / 3600 or a 9600k is probably what you want.
If you have a 60hz monitor, and generally push the in game quality settings as high as you can get away with, maybe apply a little AA, etc, and don't play much for esports games then you don't need a very fast CPU at all.
In this case, a first gen Ryzen quad core (r3 1200), or say an old 2500k will be enough.