Having more than 60 FPS in itself will not yield any results, however, having a GPU that can render at more than 60 FPS is good because it means that if there are slight variations of FPS, it'll keep up and not go below 60.
When you're playing any game and lots of visually-intensive things start happening FPS will drop. If your GPU was struggling to stay at 60 FPS while you're doing nothing, it won't keep up. However if you were with, let's say, 100 FPS, you'll almost certainly stay above 60 FPS no matter what just happened in the game.
And having FPS above your refresh rate also has a negative impact, which is corrected by vertical sync, in which the graphics get teared. Vertical Sync locks your max FPS to your monitor's refresh...