No, in most cases they are not appropriate for public sharing. These stories often involve personal and private aspects of a relationship, and sharing them publicly may violate the privacy and dignity of the individuals involved.
It depends on the nature of the story. If it's a light - hearted and innocent 'naughty' story, like a wife playing a harmless joke on her husband, it might be okay in a very friendly and private gathering. But generally, public sharing is not a good idea as relationships are private matters.