There is a reason why (at least where I'm at) it it illegal to hold and talk on a cell phone while driving. Not that hands-free talking really makes any difference.
One loses efficiency or what-have-you when attention needs to be shared amongst different activities that require cognitive control. By shared I mean more that time slices need to be divided amongst the activities. Attention is really a fascinating thing.
I can mindlessly listen to music while studying. But I know that I really don't pay much attention to the music, especially because most often I choose to listen to songs I know well and really like.
Can one really "mindlessly" play the accordion? Other than the physical movements that can in a sense be automatic, can one really determine what notes to play "mindlessly"? I am trying to picture a musician who has painstakingly spent hours upon hours memorizing a piece of music and I guess one's playing can reach the point of almost "mindless" playing.
Even if so, I think the attentional resources that studying demands would not allow enough attentional resources for playing an instrument...