Well sure you can run the pump, but the surface action of the skimmer won't be particularly stellar since you have a cover on top holding surface schmutz in place?
Make sure no small piece of cover can block the skimmer if that is your only source of water to the pump, or you'll run the pump dry. Uh Oh!
If a cover is on, and in contact with the surface of the pool water, it is impossible to skim the surface.
The skimmer will function fine as a water return to the pump as long as the cover does not block water flow into the skimmer, and the water level is high enough that the pump doesn't starve from lack of flow.
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