Hogan's Heroes was from 1965, it's possible they were parodying that in spirit (but using the 'wacky family' structure of any number of bad sitcoms from the era)
Adams is technically only ever credited by the Pythons with contributing to two sketches during the course of the whole series, and this is not one of them. However, it's entirely possible that many of his ideas made it into the show since he was good friends with Graham Chapman (who wrote a lot together hoping to one day do a show together) and well liked by the rest of the group.
The one where the bleeding patient has to fill out forms while he's dying and I believe he's credited on a writer in the Mr. Neutron episode as a whole. He also appeared on screen in a few roles, but which ones I honestly don't remember. I'm sure it's on a wiki or something.