For someone who claims to never scheme, Joker's one hell of a planner.
Anyone who took that scene at face value didn't understand the Joker at all in this movie. JOKER LIES. When Joker says that crap he's not talking about himself
at all he's telling HARVEY what HE needs to hear in order to turn him. All that stuff about having no plan and fate being the only fair thing and forsaking your own schemes and plans is a straw man, so Harvey will embrace his duality fixation and go nut fuks. The last thing Joker wants is Harvey to stop and think who
planned everything that just happened to him, so he gives Harvey a shove in the opposite direction (where Joker knew he was already leaning).
ALL Joker ever does the entire movie is scheme and plan. A viewer can be excused for confusing it
in the moment, just like when he tells Gambol about his father you think for a moment he's telling the truth. but as the movie goes on you realize he was probably talking about GAMBOL's father just like he was talking about RACHEL herself when he told the story about the faithless woman. he just says the most mocking, hurtful or emotionally crippling thing he can think of at the moment. viewing the rest of the movie unfold, it's clear how what Joker says to Harvey about not having a plan is just part of the plan
As for does Joker know Batman is Bruce Wayne. LMFAOOTFRALMAO. Joker will never know that for the same reason he could never have predicted how Batman would DESTROY Joker's plan by being altruistic and taking the fall for Dent. Joker
thinks he knows Batman and that they're kindred spirits but he doesn't actually know the most important thing about Batman. Batman isn't about darkness... the vigilantism, his parents' murder, the anger, the vengeance. He's about a way through that darkness, fighting through it to the light at the end of the tunnel. Joker's world view does not allow for a truly selfless being... those who are noble are simply frauds or lucky... when push comes to shove they will fall like the rest of us.
Actually to him, Bruce Wayne would make sense. In a way he's a man who's embraced total nothingness like Joker. He's a man who has the wealth and the means to do
anything yet does
nothing. That's the type of lost, desperate, man whom Joker would consider actually correctly enlightened. Also Joker would appreciate the fact that Bruce is totally open and honest (esp to himself) about his misanthropy.
Batman... would not make sense to Joker. It would ROCK HIS WORLD. The idea of a man who starts with everything and gives up EVERYTHING for others, and to not "want" anything from that... to the Joker a man like that doesn't exist. Because goodness does not exist.
The reason Joker thinks he knows Batman is because he can correctly deduce his superficialities. For example there's no question he knows Batman has a relationship with Rachel. BUT the place Joker takes it is dark, evil. He automatically assumes it goes to Rachel's LACK OF VIRTUE and FAITHLESSNESS... basically her being a two faced ***** and a ****e. Where he takes it makes sense in Joker's world view. An example of a supposedly righteous woman who goes around with Dent while the Sun is shining and the camera is on TV, yet behind closed doors is ****ing someone else. The idea of the sublime nature of Bruce and Rachel's relationship where not only are they faithful, but lean on each other and implicitly trust each other with their lives and everything important... Joker could never get.
Because of the superficialities Joker can also anticipate and manipulate in large degree Batman's own actions. However his ultimate totally ignorance of the most important aspects of Batman's character makes Joker's ultimate defeat at the hands of the Batman... not only in this movie when Batman takes Harvey's guilt but in the comics and in every future movie... inevitable.
Now if Joker was somehow more like the Riddler, and could actually take an objective look at Batman as opposed to an insane obsessed one then yeah he would have a chance to figure it out... he's THAT smart. And thus he could probably "defeat" Batman as far as Batman's ultimate goal. But he cant, he doesn't and he wont. The End.