It's entirely possible for any cpu to become a bottleneck, try gaming while rendering and streaming. So the realistic answer is Yes its possible, especially at low resolutions where the game is more cpu dependent. Throw enough scripted mods at some games and fps will drop, enbs etc. Not that hard to bog any cpu down.
But just running simple games? No, the 1080 will generally have higher usage as ppl tend to use higher graphics settings, but that's on the user, not the cpu/gpu