I think the 'as many as Dan' should actually be 'as many as damn', since that's a catchphrase meaning broadly 'a helluva lot'. Whether it would have been Bowlderised to 'Dan' in the early 1800s I don't know.

I first heard the song from the Dubs singing, on the 25th anniversary album and found it hysterically funny. It seemed to me to be a music-hall comic song about how laughable rumour can become as people, working from fragments of information for which they have no context, sensationalise them when they pass them on. In this case the tinker, who's illiterate, hears about the steam engine being the making of future generations, but has no idea what that means. So he "fills in the gaps", saying that it's about making babies by steam because that makes it a better story than just passing on the bare bones of what he heard.