Does the joker really die in batman arkham city?

That question is a mystery to many, because while it is said multiple times that batman and his companions(robin, nightwing, etc.) are sworn to never kill, whenever you play as robin in a predator map you can argue against that. For example:if you perform a window takedown while playing with robin he will pull the thug through the window and wrap his legs around the thugs shoulders and throat area and twist them, seemingly breaking his neck which would lead to death. You even hear a cracking sound.