Most any bike rack for the car says in the manual specifically not to do this. Due to wind drag not just from motion of the car but from side winds or gusts from trucks also.

If you worry about rock chips for stuff going over the roof of a car, then get a rear mount instead.

But don't cover. The only time people really use those is if they lock a super beefy cable through the frames and a cover for storage overnight at a hotel or something.