Yes, when Holly showed up in Port Charles she was working a con, with her corrupt family, but she fell in love with Luke and went on the run with Luke to escape her cousin Basil and the rest of her family. Later, she was happy as the police commissioner's wife and helped Robert solve crimes.
Having her still running scams at age 65 is absurd. And she would never have abandoned her daughter. She, in fact, helped raise Robin with Mac when she returned to Port Charles in the early 1990s.
Recently, Sasha said that she was raised by her grandmother. What grandmother? Holly's mother died with Holly was young.