I'd definitely assume the Joker would have played a role had Heath survived - for one thing, unlike Ra's al Ghul and Two-Face, he didn't die at the end of the movie.
^ Including the Joker in a priosn break would have been problematic because they wouldn't have been able to have him in make-up.
He'd be part of the prison break, probably not show his face (but hear his voice) and he'd then appear some time after in Joker costume. Who's to say how the anarchist would really take Bane? He could fight Bane because that's kind of how he rolls. We could even be in a situation where the Batman kind of needs Joker in the Bane thing (in the sense we saw him need Catwoman in this movie). Lot of ways the movie could have played the Joker's role had he been there.
It seems to me that the simplest way to fit the Joker into the plot of
The Dark Knight Rises would have been to replace Talia's role at the end (the person secretly involved in everything, the secret point of Bane's plot, and then the one driving the bomb to try to keep it out of Batman's hands) with the Joker. Say, Bane reveals that his plot all along was to foment the kind of chaos in Gotham that the Joker would take advantage of -- to be the man who deliberately unleashes the rabid dog again -- and that the wanton death and destruction is something the Joker wants to preserve.
It would also nicely dovetail with the idea that Bane was kicked out of the League of Shadows; the League's goal is to "restore harmony" by taking down the world's most powerful and corrupt power centers like Gotham, but if Bane's goal is to unleash the Joker's special brand of anarchy, that explains why he'd be kicked out.
As it stands, Bane's and Talia's motivations don't quite make sense, I think. We're told they want to bring harmony by bringing down the corrupt, and yet they still want to destroy Gotham even after bringing down its corrupt aristocracy. It would have been fixed by something as simple a line as, "See how corrupt Gotham is? They let their plutocrats rule with impunity -- and when I bring down the powerful, the people become just as corrupt as their former oppressors! Gotham must burn." Or some such.