Can you run pool pump with vinyl tarp style cover on the pool. This cover drops down into the pool approx. 6-8 inches by design.
Sure, a pool cover doesn't bother the works at all. Most outdoor hot tubs are designed to have a cover over them while waiting for bathers to show up.
If there are any aerators, I would close them if it will be running for more than a few days without the cover being removed—to keep it looking nice and smooth. Otherwise big blotchy bubbles form.