Hi DrunkLahey. The radio antenna allows your car to receive a better reception signal.
If you live in an area with strong radio signals, you will not notice much difference in reception by removing it. However, if you were to drive further from the signal source, you will lose the signal quicker than if the antenna is present.
If you drive around the same areas every day, don't usually venture far, and generally listen to stations with strong signals in your area, you'll have no problems, since you seem to live in a strong signal area. However, you will not receive stations with weaker signals. And if you take a long trip, you will lose radio stations sooner than you will with an antenna. And without the antenna, you won't receive new signals until you drive closer to the source on a trip.
If I were you, I would just leave the antenna in place. However, if it is bothering you and you want to remove it, then yes, you should cover and protect the antenna base from the elements.
Keep us updated and good luck.