Should preform around the same as an fx 8370 so yes it will work, but do not expect anything mega out of it.
More in depth info here: http://www.pcgamer.com/intel-pentium-g4560-review/
Honestly the 4770 ain't bad so you will survive on the cpu / mobo / ram until we see how Zen / intel response is. With your GPU upgrade it should make it very decent.
Might be PSU related as i cannot remember what the 660 recommended PSU was, that along with the powerdraw from the CPU might be a bit much for a 550w, just a guess.
What is your current build looking like ?, if you are using a site to build / order your rig it would be easy to see what it comes down to without graphics card.
I.E how much are you spending currently without the graphics card.