i just can't understand why people have think they know what bottleneck is...
Bottleneck its a drop in general performance due to one particular piece of hardware not being able to keep up with the rest of the system.
A good example of bottleneck will be 4gb of ram for modern games like GTA V... the lack of ram might cause several framedrops and thats the way bottleneck works.
On the other hand the different hardwares have different performances, and that statement its more accurated when the particular software its added to the mix.
So depending on particular software and the ammount of process being executed by the system the Fx 8xxx will work closer to i7 or closer to i3 performance... BUT
there's no reason to think Fx8350 will bottleneck GTX1070, since it can handle GTX980 in 2x SLI. And on the other hand that's not the same as saying Fx8350 will get the best results out of the GTX1070 for every single game.
So to the very specific question made on this topic, NO, there's no real need to change your CPU in order to make the GTX1070 to run at his max. Even with no overclock, but again, a little overclock will indeed help.
I would keep posting links to validate my points of view, but noone cares, all the fanboysm its quite fact-proof.
PS: if the question where talked about GTX1070 paired with i7 3770k at stock i would have answered the same, and that CPU its the closest Intel counterpart of the Fx8350 (and i love that i7, for the record)