When he enlisted, he signed on to obey the lawful orders of those appointed over him and to be subject to the UCMJ. Things that are legal for civilians are illegal for military members, including trying to quit a job or failing to show up when required.

The Navy term for AWOL (absent without leave) is UA, for unauthorized absence. This is covered under Article 86 of the UCMJ. If all he did was go UA, then he would likely be subject to non-judicial punishment (the Navy calls it Captains Mask) which could result in loss of rank, pay, and limited confinement. However, according to the UCMJ, being AWOL/UA for more than 30 days is desertion (Article 85) - a felony with very severe consequences. In very rare cases, desertion in wartime has resulted in the death penalty, but he doesn't have to worry about that. In addition, missing a ship movement is also illegal under Article 87.

There are consequences for his refusal to deploy as ordered. Either someone else who wasn't scheduled for deployment had to be grabbed at the last minute to take his place or the other members of his department had to make up his duty hours. That means that either someone who was supposed to be at home with his family is now at sea to make up for this guy or his shipmates will likely end up working 12 hour shifts. Screwing over your shipmates is hardly the way to win friends.