I also believe, had he lived, Joker would have played a role in TDKR. Not instead of Bane necessarily, but perhaps a supporting role. There isn't really any space for him in this film, and he's so dominant that perhaps it would have been better to leave the character out, even if Ledger was still alive. Did I hear correctly that he signed on for an optional sequel? Anyway, I can imagine Joker sitting in arkham or prison feeling alittle left out.
Also, if Arkham is out of commission, then he'd be in prison somewhere in Gotham. In this case, Bane surely, surely would have released all prisoners during the city takeover. It's just logical to presume he's escaped, even if Arkham is still in commission(because Bane would have released them aswell, in all probability).
I don't think he needs a mention particularly, but i'd be happy if he was. If we get a quick shot of inmates being released, i'd love to see one brief moment of a prison door opening, and a dark, silhouetted Joker sitting in a chair, head down, then lifting his head. Of course, it'd be lit so that we could only guess who it was, but enough for the fans to recognise. That'd be cool