I ran an overclocked 7850 with a 400W seasonic gold psu.
It is borderline if your cpu and other components are not low power.
An underpowered psu will manifest itself with random system reboots/shutdowns (triggering ocp or uvp).
Usually happening when you fire up a video game, or a browser adobe flash video kicks in.
Point is, as others suggested, a quality psu will likely handle it (assuming your cpu and other components aren't monsters).
Higher wattage psu == piece of mind