The FX 8350 will limit your GPU; it already limits a GTX 970 in many circumstances, but the answers is not simple, because it depends on the specific games you play and the resolution and refresh you play at.
If 60Hz, 1080p, 60FPS is your target, toy will notice the limits of the CPU more.
If 120Hz, 2K, 60 FPS is your target, you will notice the limits of the CPU less.
No matter what, you should be planning for a CPU/Motherboard upgrade. Even overclocked, the FX8350 is, at best, a mid-range CPU, well suited to your GTX 960. Today, Intel is the only game in town. Towards the end of the year, and if the rumors are true, AMD's Zen will provide a low to mod high end CPU suitable for use with a GTX 1070 and demanding games and circumstances.