The answer is yes, no, maybe, and sometimes, because CPU and GPU load are largely unrelated. If you're aiming for 144hz gaming, no CPU will get you to 144fps in every game but in the vast majority a modern i7 will get there. If you're going to be running 60hz screens (let's say 3x 4K 60hz screens) even a Core i3 is enough for 60fps in most games, though an i5 would be a safer bet.
The amount of GPU power you have is irrelevant to bottlenecks. You need to buy enough CPU power to hit the framerates you want in the games you play. You can always get there with a GPU by lowering the graphical settings, more expensive GPUs just let you run higher graphical settings.