If they do then it's a bit confusing for them both to look, sound and act like the same person.
I still think it would have been much better if he'd played Dr Jekyll as himself and Mr(s) Hyde as Trans Eddie then there would have been an obvious transformation - and there would have been a element of Psycho about it as well when Bates dresses up as his mum to do the murder.
They've missed a trick IMO.