You could do if you wanted - but remember an interactive story is for everyone, and when someone adds a chapter, it may not go where you want it to.
The only problem I've found with the interative stories (well, it's not a problem, just an opinion...:P) is that some people consantly add their own chapters. I've only followed a chapter written by me by another written by me when I want to get a story going in another direction - I just think that people should write their bit, then leave it for someone else, or the story doesn't become quite as interactive as it should be, if you get my gist. :)
On another note, I too write fanfic - but it's definately drama, not comedy, and mine is for
Star Wars.
If you don't add your fanfic here in the form of the start of an interactive story, how about leaving a link to somewhere on the web where people can go and read what you've done? Do you put them onto the
Fanfic Net or anything, for example?