I think the utmost classic appearance of a sitting politician in a public forum was Richard Hatfield, on Air Farce. His role was that, on cue, he would walk out on stage, and say 'Hi!'.
They started the skit with some chatter, and right on cue, one of them said, 'And how are you today, Mr Hatfield?', at which point he appeared and delivered his line...it was priceless, coming not long after his incident with his luggage during the Queen's visit. The crowd absolutely roared, and once he got over the shock, he lauged, too.