For people unfamiliar with the site, it is an art project where people write secret son postcards and send them to a guy who archives them. He posts a collection every Sunday, has released books, and does speaking events. The main site isn't something where people go post whatever they feel like. Sometimes they are goofy and about little things, some will rip your heart out.
I don't think it is possible for art to be rude, especially when it is a submission to a collection that is supposed to be about baring it all and letting down boundaries in a way that can only be done anonymously. I can see why you may think this is tasteless, but the point of post secret is that you can send in anything at all. Its where people get bad things off their chest sometimes, and that postcard made me think so it served its purpose.
If the man sees this an realizes it could be him, I don't think that is really changes the situation for them that much. If it is possible for you to have a child with a woman that you wouldn't know about that postcard wouldn't make that more likely. You still had relations with a woman either casually or ended it so badly that she wouldn't tell you, so all this would do is remind you of that.