It depends on the game itself. Most games do not care how powerful the CPU is as long as the GPU is not the bottleneck. Most game are not limited by the CPU; though a powerful CPU improve average FPS, but it generally will not be noticeable unless you use benchmarks (meaning less than a 10% increase in most cases). The type of games which are usually limited by the CPU are strategy games because there are a lot of calculation processes done by the CPU behind the scenes. Most first person shooters are not limited by the CPU, but there are a few exceptions like Fallout 4 and Skyrim.
Overall though, I would recommend that you upgrade CPU though because at the very least it can improve minimum FPS in games and it serves as a good basis...