I also think a group challenge is a cool idea. I agree about the high possibility of group members bailing out before the projects are complete as stwert mentioned. I personally don't mind bailing out of a competition when other stuff comes up or if I lose interest, however, if I'm part of a group that is relying on me, I stick it out til the end at all costs.

Hopefully, as honestdom said, others would be more willing to finish as well, especially if it's not to daunting of a project.