Covering Airing Vents in Floor
Your heating/ac system was designed to distribute “conditioned” air (heated or cooled) throughout your house. Covering a few registers will cause air to be redirected randomly to other parts of your house. This causes over-heating in some rooms and over-cooling in other rooms, depending on what the thermostat is calling for. 

Yes, you can remove the existing damaged ducts and reinstall a new balanced system and cover the registers that are in the wrong location. However, the new ducts will need to be sized properly. I’d have a reputable heating and air conditioner contractor layout a new system. If they can’t, I’d contact a mechanical engineer (not civil engineer).

We’ve done this many times and we always search out and find where the rodents are entering the house and the system. As @Ed Beal said, rodents will tend to return to a warm environment.