Can you run a pool pump with a cover on?
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&mdash;to keep it looking nice and smooth.  Otherwise big blotchy bubbles form.