I have a 7600k and a 1080 GTX, so I can answer this question. It works fine for most games, but I have to limit the FPS in Battlefield 1, or else I get 100% cpu usage and it eats my inputs. Mafia 3 and Ghost Recon Wildlands also gets the same thing. 100% cpu and it sometimes eats my keyboard inputs or stutters.
Don't even get me started on streaming. I can't stream for crap with this 7600k. Even some crappier games have problems streaming with it, although those might be more due to optimization. I can stream Doom(2016) just fine, but I cannot stream BF1, because it eats inputs and basically destroys the CPU, even at low settings. I ordered a 7700k, because screw this.
Take it from me, if you play some of these more demanding games, a 7600k will definitely bottleneck the 1080 GTX.
I am running at 2560 x 1080 resolution, with 16 gb of DDR4 3000 ram and a hybrid cooled 1080 GTX. Also overclocked the 7600k to 4.8 Ghz, and it doesn't alleviate the problem at all.