Well, Saturday Night Live did - and does - that kind of thing all the time.
Indeed so. SNL has done some famous and beloved Trek sketches, notably "The Last Voyage of the Starship Enterprise" with John Belushi as Kirk, Chevy Chase as Spock, and Dan Aykroyd as McCoy (which you can watch at Hulu
). When Shatner guest-starred in the '80s, they did a great sketch called "The Restaurant Enterprise," with Shatner as Kirk, Kevin Nealon as Spock, and Dana Carvey as Khan, the restaurant inspector (and with the guy who played Sulu in "Last Voyage" reprising the role). They also did a T. J. Hooker
sketch in the same episode.