It's definitely against the rules, too. Statute 346.79(5)
"No person may ride a moped or motor bicycle with the power unit in operation upon a bicycle way."
Perhaps I haven't seen him, though. I've seen a guy on the bike path that is between John Nolen and Lake Monona, but not really on the Capital City bike path proper. I think. I don't know the names too well. I come from the city and go under the beltline, then turn on Industrial Drive to go to work. I'm pretty sure the Capital City path starts right there on the other side of Industrial Drive.