I think if Batman died the Joker would feel something but not allot. He would be pretty much free to do what he wishes in Gotham city. Yes he would have lost his long time foe causing him maybe to be depressed for a short time, but in the end things would be for the better for Joker and he would most likely be happy.
Joker would feel like a fool and probably commit suicide. Joker just wants to have gay sex with
batman but he doesn't know how to say it and he just picks on batman. If he really wanted to get
away from batman he would move to LA.