Do you really think that Heath Ledger would have won or even been nominated if he hadn't died?

Don't get me wrong, I thought the Dark Knight was amazing and that Heath Ledger was amazing BUT one of my teachers made a comment the day after the Oscars "Would Heath Ledger have won if he hadn't had died?" and it got me thinking, would he have won? I mean the movie was shut out from Best Picture (for something like The Reader, seriously?) and was basically up for like tech awards. What do you guys think?