I'll go with no. I do not think that he has any actual wish to die. I think he doesn't much care about what is happening to him, but I don't think he wants to die.
If he wanted to die, he could have done it easily enough. He could have, for example, really tried to fight the elevator guy who is also a pimp. If he had really fought hard, the guy probably could have killed him.
All that Holden ever does is sort of careless -- how he stays out in the bad weather and gets sick, that sort of thing. But it's not the sort of thing that's likely to lead to death.