You could try it out for awhile but keep track of your stock level. If it starts to drop then institute a '1 for 2' or '2 for 3' plan where people have to contribute punctured tubes to get patched ones (some will not be patchable, so '1 for 1' might not work).
Lots of cyclists never patch tubes and just toss them, so you'll probably get plenty of material for this project. I've become known as someone who patches tubes, so I'm given quite a few when flats happen on group rides. Use some myself and also give out some when I'm driving sag for the supported century put on by the club.