No, it would not. Morrowind and Oblivion both have the construction set used to make the game in the PC version while at the same time there is an Xbox/360 version without it.
What happens though is that I can load my saved game and I can play for a while without the error but when I try to start a new game, I get it. I just reinstalled and the same problem persists.
Alright, the error appeared once as I was playing the game and I had to close the game. Now it happens whenever I start the game (the loading time after the menu)