Should you cover bathroom fan with vent cover?

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 :-)