I was so certain that Snape wouldn't die in this book that I missed entirely what you saw in Chapter 2, but of course, you're right: he thought he was sealing his own death warrant. Had I somehow been clued in to the uncomfortable reality that books 6 and 7 are really one, not two, I might have seen it differently. I think that scene does ultimately set up both Snape's "betrayal" of Dumbledore and his own death that is the probable end result of his committment.