My short answer: Of course not.
But…..
News reports indicate that the captain of the Korean ferry that capsized got on to a lifeboat before passengers and the article asks if Captains do have to go down with the ship. This brings us back to the cruise ship disaster from two years ago involving the M/V Costa Concordia where that Captain infamously abandoned his post despite the, ahem, urgings of the Italian Coast Guard.
This begs the question: Would the Captain on a U.S. flagged vessel have a duty, legal or otherwise, to remain onboard a sinking ship?
Consider the case of Seaman Alexander Holmes, a deckhand on the M/V William Brown. The William Brown was on a voyage from Liverpool to Philadelphia when it struck an iceberg and sank. Some of the crew and passengers, including the Captain, made it into two small boats. After many hours in one of the small boats, the weather turned poor and the boat was in danger. The First Mate was heard to say "Men, you must go to work, or we shall all perish." Seaman Holmes then forced 12 men out of the boat. Others went into the water and all who did died. Later that day, the survivors were rescued.
The survivors made a complaint in Philadelphia and Holmes was accused of murder, but indicted for manslaughter. He was convicted and sentenced to six months in jail.
The Circuit Court of Appeals affirmed the conviction and found that Holmes had a duty as seaman to his passengers and that usurping that duty, leading to death, gave grounds for a manslaughter conviction.
The Court said:
It is, said the court, the municipal of civil law, as thus comprehensive, as founded in moral and social justice,–the law of the land, in short, as existing and administered amongst us and all enlightened nations,– that regulates the social duties of men, the duties of man towards his neighbour, everywhere. Everywhere are civilized men under its protection; everywhere, subject to its authority. It is part of the universal law. We cannot escape it in a case where it is applicable; and if, for the decision of any question, the proper rule is to be found in the municipal law, no code can be referred to as annulling its authority. Varying however, or however modified, the laws of all civilized nations, and, indeed, the very nature of the social constitution, place sailors and passengers in different relations. And, without stopping to speculate upon overnice questions not before us, or to involve ourselves in the labyrinth of ethical subtleties, we may safely say that the sailor's duty is the protection of the persons intrusted to his care, not their sacrifice,–a duty we must again declare our opinion, that rests on him in every emergency of his calling, and from which it would be senseless, indeed, to absolve him exactly at those times when the obligation is most needed.
Ironically – Holmes had demonstrated great courage during the sinking and was the last person to abandon the sinking ship.
As to the Korean ferry captain or the Costa Concordia, crises are the times that seamen train for and if the most experienced person onboard abandons their post for the safety of a lifeboat, tragedy will certainly ensue.