Did ahab kill Moby Dick

On the 3rd Day; Ahab is taken out of the boat, when a rope (attached to a thrown harpoon) leaving the vessel catches him around the neck, and he is yanked out to his death. Then a swipe of Moby Dick's tail fluke sends the boat in the air and the crew is thrown into the water. Only Ishmael survives, kept afloat by Queqod's coffin. He is eventually reduced by the Rachel, still looking for people from their lost lifeboat, including the Captain of the Rachel's son.