He doesn't care whether Batman beats him to death but he's not depressively suicidal. Whatever happens, happens: the means justify the ends but the ends are also important, and they're all about destroying Batman's or Dent's moral compass, not about ending the Joker's own miserable life. That's the distinction. The end of his own life in either case would just be collateral damage, and in other cases, he seems to have pretty good survival instincts. And frankly, in the assassination plot, he seems to have chosen a thug who physically resembles him to stand by him in the honour guard, perhaps realizing in any ensuing confusion, the other guy might get shot and enable him to get away.
There seems to be an insistence, because Alan Moore's immortal Killing Joke was cited as an influence, that this Joker has to be that Joker. But he isn't. Moore's Joker, despite the horrible things he does to Gordon and Barbara, is essentially pitiable (and even self-loathing and remorseful), and Batman still seems to think he's redeemable. There is some influence, in some of the motifs and details, but TDK is hardly based on it. And for that matter it's also influenced by material where the Joker is far less sympathetic, like Arkham Asylum. (In fact, I actually find this Joker more like that one, though not as philosophical, and certainly not as sexually ambiguous.)
However, all that said, even if he doesn't need to have had a pity-inducing past (does anyone watch Pan's Labyrinth and do anything but cheer when Mercedes gives El Capitan half a Chelsea Smile? yes, it's a horrible thing to have done but she's desperate and has to work fast and he is about to torture out of her information that could kill all her loved ones), that doesn't mean he isn't likeable, not in the sense one might like a future best friend, but in the sense that he is captivating: you cannot take your eyes off him, no matter how disfigured he might be or what horrible things he does.