Okay, I have never taken one of those apart, but I see no reason why not...
An X-box is pretty much just a video game computer, right?
All computers and laptops I have ever messed with have some type of ribbon cable going to extra hardware like DVD drives, Floppy drives, stuff like that.
I would say as long as the drive will fit, and as long as the ribbon cable is the same size and pin pattern there is no reason why it wouldn't work. You should be fine.