I run a 6600K i5 at 4.6Ghz, and it cannot bottleneck my GTX1080, even it is heavily over clocked too. And this is playing at 1080P also. Just about every game is running around 180-300 frames per second maxed out at 1920*1080.
99% GPU utilization!
If I were to run SLI GTX1080's this is where i would be in trouble at 1080P, 4K would fix it though.
A 6600K will offer a huge boost over a i3, I think it is all that is ever needed in a CPU. I use Sony Vegas pro 4-6 hours a day for work, rendering 4K video. It just flies!
I also use shadow play, and I record 4K gameplay.
My 6600K at 4.6 is always butter smooth no skip, no lag, no studdering. Just SMOOTH!
I could get a 6700K but I just don't need it!
And I encode videos happily with my 6600K.
It opens up a lot more doors for you than to just be bottleneck free with your gtx1060.