Considering this year's Oscar contenders haven't emerged yet, I don't think anyone can assume he will be nominated.
But if by some twist of fate this performance is nominated, he will not win. No way. This is not the type of role the Academy goes for, and why should they? Because he died? How many talented actors in non-Oscar-baity roles have been nominated for an award, let alone won?
The only nominee I can think of in this situation is Anne Ramsey from "Throw Momma Off the Train."
The last winner to win an award posthumously was Peter Finch for "Network," and he gave an astounding performance. His death wasn't the sole reason for either his nomination or his win; it was his performance.
The Academy isn't sitting down and drooling in anticipation over "The Dark Knight." And after it comes out, and has its dues at the box office and with fanboys, they'll likely forget about it.
Sorry, but that's just how it is.