Hmm.... good idea. Hope it goes well.
Sounds very similar in concept to The Thread, which is run on
www.Lit.org (this forum's sister site). The Thread is a collaborative story or poem, which people take turns at joining in with. It does need someone in charge to allocate the parts, otherwise you end up with two people writing the same section (actually, that's pretty much the same with open source software, too), but it is a really fun thing to take part in.
Take a look at the recent Threads on Lit.org, because there have been some good ones in the last couple of months.