Think one of these is powerful enough to make a NAS into a music server?
All it needs to do is run one program.
Sure! It's actually a fairly powerful Linux platform. It can probably BE the music server, actually, instead of using it to front a NAS, though that should work as well. A Google search will turn up a number of people doing this, and the software needed.
Here is one source for Pi music server stuff:
http://www.raspberrypi.org/phpBB3/viewtopic.php?t=6803 You should be comfortable with hooking things up and it would definitely help to know some Linux. To date, nobody I know is providing a "plug and play" solution for the Pi, even the so-called "complete Raspberry Pi" kits you see on ebay and other places still need a case, video/keyboard, etc.