I am not 100%, but I believe the covers over the neck pickup are mostly for asthetics. Some players may use them for reference points or rests, but there should be no discernable tone difference.
If there is a cover on the bridge pickup, it may be just for asthetics, but it may also be hiding a piece of foam laying under the strings which helps accomplish a thudier, less sustained, Motownish, Reggaeish, Uprightish tone.
