Although you will get bottle-necked in quite a few titles..I still don't see an issue running both of them together.
Like, 13thmonkey said, you would have to upgrade the rest of your components to suit the i5 6600k.
Will you get better frames and stabler game play with the Intel CPU? More than likely. Is it worth it? That depends on your budget and if you feel that your experience playing games right now isn't what you want.
If you want to alleviate the bottle-neck, I suggest overclocking your CPU if the motherboard is of high quality.