Steve is one of the three or four most helpful and most knowledgeable people on this site. Apparently he has taken to drink. I am one of the people who has tried to remove paint from brick. It can't be done. If you are certain the brick will never be presentable as bare brick and that you will always love the color you decide to paint it and that you will not mind that from now on this formerly no-maintenance wall will require maintenance, then, yes, painting it is a great idea. I would first try covering the carpeting very carefully (maybe taping plastic drop cloths to the carpet and covering those with canvas drop cloths) and trying to enhance the brick by chipping off the old mortar and cleaning the brick.