Nope. No need to fill the sump to the rim... leave yourself some safety room.
I run my sump at a level that (A) suits the equipment running in the sump, skimmer, reactors, etc... and (B) insures that no air is sucked in at the return pump. Any higher than that is unnecessary.
When the power is off, and all water that is going to drain into the sump has done so, I still have several inches of sump capacity left. That's just as it should be.
Oh... if you're relying on anti backflow valves to keep water from draining into the sump... don't. Force them to fail, because they're almost guaranteed to do so at some point, and you _really_ don't want to flood your sump.