It seems like it would be pushing it a bit, but that PSU is rated for the full 360 watts on it's 12v rails alone. I know my own 3570k witha GTX670 only pulls a shade above 300 watts from the wall, which is about 270-275 delivered to the machine... Your design would put it at pretty similar power usage, and 275 watts would be less than the 'rule of thumb' 80% capacity.
You'd be really cutting off your upgrading options though, but it should power it just fine.