Not exactly. “Gigolo” implies that the man is supported by the woman, or is in it strictly for economic reasons; and the woman who supports him does not necessarly have to be married. Therefore the relationship is not necessarly “illicit.”
While “mistress” does to some extent suggest that the woman is supported by her lover, this is not necessarily true. However, the word does imply that the man be married.
From Merriam-Webster