When I was at college, some of my fellow students would take wet prints home in paper packaging bags. I wouldn't recommend that though - it's too easy to wreck the prints. I think your suggestion would work if you could ensure the prints did not dry out or get knocked about in transit. Leaving a little water on the prints would obviously help. FB prints come apart easily when wet, but if they dry out you'll never separate them without damage - been there, done that! When you get home, soak the prints as soon as you can. Do a trial run with some duff prints. It's hardly ideal but I don't see why you couldn't make it work.
Alternatively, have a chat to the club officials and see if there's somewhere you could leave prints to dry overnight. Maybe they have an old flatbed dryer lurking about that you could use - they're brill for getting prints flat too.