I do not remember Jack ever checking Naomi. If he did, you would think he would have figured out whether or not she was dead. If he thought she was dead and she crawled off, he would have been more freaked out. If he knew she was alive, you would think he would have tried to help her rather than leave her laying there in a bloody heap.

Jack has been consistently moving towards a more aggressive, violent nature. Maybe he has felt it was necessary to survive. But, he cut Ben's kidney sack on the table and would have let him die if necessary. I am pretty certain he had every intention of killing Tom, and Ben after the rescue as retribution for what he thought happened to Bernard, Jin and Sayid. He also fully intended to kill Locke in that moment, because Locke had undermined him at every turn in trying to leave the island. I think Jack had spent his pre-island life suppressing his anger and frustration. Now in this situation many of his actions and strength are fueled by pure rage. Could be helpful, could be his undoing.