well you will actually have to play it on the xbox for it to work, it's not compatible with the 360 unless you override your 360 with third party software, which is against the EULA.
You might be wrong on this count, I'm pretty sure if you search for compatable original xbox games for the 360, Morrowind will be in on the list,
"how do you know?" I hear you ask.
"Well cause I have just loaded it up and am currently playing it fine" I reply
They do state that you may fine some occational glitches, but nothing game breaking or that a reload wouldn't fix. But so far I have not seen a thing, and have been playing it on the 360 on and off for a couple of years.
I think there is a compatability list on xbox.com somewhere