Will the processor become a bottleneck for the graphics card?

Question

Iron

Hello. I have not been interested in hardware for a long time, a long time ago I assembled a computer on a core i5 3570K and only changed the video cards a couple of times.
Now I sold my 290X and I want to buy a gtx1070. I doubt now whether the processor will become a "bottleneck" in this bundle?
Or take 1060 and not bathe? And it's cheaper and I have FullHD only, I don't plan to switch to more.
If anything: overclocking mother - gaming, brains (of course ddr3) - 16GB.
System on two SSDs in RAID0