A hard drive is a hard drive, it either works or doesn't. If it's working in your 360 it should be OK for backwards compatibility.
Is CJ definitely backwards compatible? If it is, you should be able to put the disc in the tray, and when you go to run it, you download a ~4gb 'update' (which is really the full game content adapted to a 360 compatible format), and should then be able to play it.