well, it doesn't really matter. the ipod app is designed to run in the background, it won't drain your battery as long as you don't play any music.
the thing is this: the ipod app is (for some strange reason) designed to always be running, it doesn't save it's current state to a file or something, it always keeps it in the RAM. that's also the reason why, for example, your currently playing playlist disappears after a reboot.
unfortunatly it also means that every time you reboot or your ipod app crashes, all your playcounts, skipcounts etc. since your last sync with itunes are lost. unfortunate design by apple, they never changed that for some reason