Does Fortunato die at the end of The Cask of Amontillado?

It is heavily implied that Montresor does bring about the death of Fortunato. Although he does not personally deliver Fortunato's fate, Montresor does put his victim in a situation that will inevitably kill him: Fortunato is chained to a wall, and then entombed in underground catacombs for fifty years. Even if Fortunato found a way to survive starvation and dehydration, he would have died of oxygen deprivation shortly after the completion of Montresor's masonry.

Then again, maybe your question regards less the possibility of Montresor's death more than it does the ethics of holding Fortunato accountable for the fact of the event; if this is the case, my personal response would be to assert that Montresor, having maliciously premeditated the execution, is fully responsible for coercing his inebriated victim into a premature burial that was sure to bring about death by asphyxiation, dehydration, and/or starvation. I don't believe Poe ever definitively revealed the chronological and geographic settings of this story, but I do know that Montresor could have been held accountable for this crime of first degree murder in a United States court, even now -- first degree murder, to my knowledge, has no statute of limitations -- so, as of this writing, the American justice system agrees with my personal judgment.