I for one cannot. Music wrests my attention too aggressively from anything else I might be doing. Most of my coworkers have music going in their headphones all day. I can't comprehend it. I wouldn't get a darn thing done.
No. I can't do anything at all while listening to music. Maybe wash dishes or clean my desk, something like that.
Another related question would be: what do those that do listen to music while studying feel it gives them? I know there are people that really need that background muzak running in order to complete non music related tasks.