Yes, it is possible for a married man to love you, even if he is in a seemingly happy marriage.
While someone might be happily married, the reference states: "Yes, someone can experience romantic attractions outside of a marriage, even if they're happily married." This indicates that emotional and romantic feelings can develop even within the confines of marriage. However, it is equally important to acknowledge that people in healthy marriages often choose to actively maintain their relationships and consciously decide not to act on feelings for others. Therefore, while the feeling is possible, the action taken is a matter of choice and commitment.