Is it a good idea to play an instrument while studying? If so, what are the benefits? We've all heard that listening to classical music and such while studying can be beneficial, but I was wondering about actually playing an instrument? If I were to absentmindedly play my accordion while reading a textbook, would it have any benefit to either my absorption of the material or ability to play music without having to focus on it? Or is this just a bad idea?

Specifically, have there been any studies relevant to this, or is there any other data on the subject?
Multitasking research suggests that people can't really multitask. I don't have any evidence to back this up, but I suspect that it's much better for your instrument skills than your studying. The accordion detracts from your focus and attention while you work, perhaps even if it doesn't feel like it. At the same time, though, that exercise may improve your ability to, say, sing and play at the same time.