Woot, longtime player, first time poster!
The problem is what being a protagonist for this kind of game requires. He has to be highly active, always taking the initiative and being one step ahead, he needs to be a natural troublemaker (y'know, so stuff like framing Pom Pom as a drug cheat doesn't look out of place), and he needs to be fairly savvy, not an idiot, but not too bright, either. And of course he needs to have lots of funny lines. The only one other than Strong Bad I could conceivably see in such a role is Bubs, and he'd need some pretty strong incentive to continually put his neck on the line instead of manipulating in the shadows like he usually does.
The most Homestar Runner would be able to carry is a quick scene or level, a la level 5 of Stinkoman 20X6.
It's okay; I'm sure you're not the first person to come up with this idea. Thing is, some ideas don't actually work in-game. I'm sure someone else here could tell you about it.