Yes, Morrowind is backwards compatible. But not the GotY edition.
GotY editon does work on the 360. I have the GotY edtion and have played it on my 360. You just need the update to allow this that is all.
It's a bit buggy at times, but it does work. Load times might be a bit long, but it does indeed work.
Also when you save your games, the pic you get from a saved game is jumbled. Funny though if you save in an interior cell like a cave or
home, then indeed you get a normal pic.
But yes it works.