The only time I ever heard anything similar was nearly 40 years ago, when one of my classmates ran into the music room, excitedly shouting, "Mr. Spencer had a baby!" Of course everyone knew that our science teacher's wife was the one who actually had the baby, but excitement sometimes makes people say odd things.I am not sure if Australian men say it, they might, but it also could be a mainly American phrase. Maybe our British, Australian, Canadian etc members can tell us they have heard the phrase used.
I have never heard a grown man claim "we're pregnant," except on some sappy American TV show.