Should you cover bathroom fan with vent cover?

The bathroom was the first one to get done... The cat box is in there so we leave the vent open 24/7/365...

I would cover it. I covered mine and it doesn't block air flow.

I would put the cover on too; they don't block that much. Plus, you can leave them open in the rain.

Yes. The fan will dissipate any odors out through the vent even if covered (as you already know the covers are vented and louvered so no rain gets in). One of our bathroom vents was not covered, and hail + wind damaged it in short order, leaving bits and pieces of the vent lid all over the roof and the screen. We had to replace the vent lid and needless to say, all of our vents are now covered :-)

my vent covers didn't block the flow that much. I'd put one on.
now if you have a personal problem you are not telling us, then put a fantastic fan in.
bumpy