Looking back, I could see Heath not winning his Oscar had he not died. I think Heath was definitely being watched closely by the Academy after Brokeback Mountain, so the fact that he gave a good performance in The Dark Knight was probably to be expected. As for his win, while the performance was memorable, in retrospect, the Academy may have foregone his win in that category, and waited until he did something else, perhaps where he was the star and not simply supporting. So in a way, I think his death did help him win, although this time around he faced little competition in that category, so it's hard to say.
In a way though, the award became more about his death and less about the film he was in. The Oscar acceptance honored his memory, rather than the film he was in. You didn't hear anyone talk about how brilliant the Joker character is, or how deserving Batman is as a franchise. While The Dark Knight was successful, I think it owed a ton of it's success to Heath. Sure the movie was awesome, but I knew so people who were completely uninterested in superhero genre films and Batman in general, and didn't even see Begins, who went to see TDK and made no bones that it was all about Heath.