Palimony is a relatively new word used to describe support paid by one person who was in an unmarried relationship when the relationship ends. Therefore, it has nothing to do with marriage. It’s an award set up by a court order after a civil suit brought by one of two people who were formerly living together who are unmarried. It is not dependent on common law marriage statutes. One of the first publicized “palimony” suits was brought against Liberace by a long term partner. Palimony is awarded to a successful plaintiff in a civil suit and is a difficult and expensive to prove.
Therefore, the answer to your question is yes. See also the link provided below for Common Law Marriage and Spousal Support.