It may, it may not. Any CPU can bottleneck any GPU. It entirely depends on the games, graphical resolution and graphical quality. Please, read here:
https://pcpartpicker.com/forums/topic/214851-on-cpugpu-bottlenecking-in-games
Also, bottlenecking is pointless to worry about as long as the CPU can perform up to your frame rate goal in the games you play, and your GPU can perform up to your visual goals in those games.
If you open the intended games with your current PC, and temporarily reduce resolution as low as possible. If the FPS you receive there is fine for you, your CPU will not cause any worrying bottlenecks no matter the GPU.