Given that the song says that the Mary Ellen Carter was a fishing boat that carried a crew of around five or six, it would make her a vessel of around 30 to sixty feet long depentant on which fishing grounds she worked,Since the song says that she sank after hitting Three Mile Rock and she lay at a diviable depth, its likely she was working te coastal fishing grounds, In which case the rock was proberly a local reference rather than one that would be found on a navigation chart.
Since the Mary Ellen Carter was a fishing boat around thirty to sixty feet long so that she would have not been listed in any register of shipping. It is a common practice world wide to name fishing boats after a Wife or a Mother.
So to see if she was real do a seach on a "Mary Ellen Carter" as a real name, rather than a boat and that may lead you in the right directions.
BTW also do a backgroung search on Stan to see if a "Mary Carter" was a part of his life.
Bruce D