There's nothing to say it shouldn't work. Drive is formatted correctly, OS' are identical and it should fit physically since it's a normal drive. There's absolutely no reason to believe there would be a problem with it.
With that said I'd make sure to get a backup of it first; just in case. Nothing should go wrong but you never know when a computer will force you to reformat or something. Even when I expect things to go smoothly I always make a backup when doing hard drive related things.