Yes, it will to a certain extent and how much depends on how CPU intensive the game is. I have an FX-8320E @ 4.4 Ghz in one of my PCs and it holds back a GTX 970 (which is about the same as an RX 470 or a little slower than a GTX 1060 3GB). It still worked fine, but the FPS drops in CPU bound parts of games was noticeable. How do I know? I swapped the card between that PC and one with an i7-4790k and played the same games. Basically, if you don't have a point of comparison like that you won't know if its bottlenecked by your CPU or not.