Apparently the xbox has no multitasking capabilities, so I'd say without programing an mp3 player into each individual game, it's not possible.
Then again I'm far from being an expert...
[EDIT] oops, a BIOS that plays soudtracks, hmmm, that might work. It might make a huge bios though.... Not that anyone cares anymore now that you can use Pheonix Boot loader.
Now that I think about it, that should be done, it would kick ass. It should only support like mp3/ogg though, none of this windows media stuff the ms dash uses.
RelaX client too maybe?
Man I wish I knew enough about programming to implement this myself