They can be kept in some reefs depending on the size of the tank, size of the fish, and most importantly what corals you plan on keeping. I have never seen them pick on mushrooms, and most soft corals grow quick enough and are hardy enough to withstand a little pick of picking on every once in awhile. One probelm however, is that they will pick on shrimp and other clean up crew members.
I have a subadult Queen Angel and a juvenile Emperor Angel, and they havn't picked on anything yet, although I'll see how that changes as they become adults and get more size on them. I know there are a few other members on the board that keep some larger angels in a reef, maybe they will chime in also.