The rubber bung is a hangover from when there used to be marks on the flywheel for setting the ignition timing on the engine. It isn't actually a plug in the gearbox itself but the bell housing where the dry clutch lives. If you look under the bike you'll see there is a substantial slot in the bottom of the bell housing between the crankcase of the engine and the gearbox, all that will happen is the grommet will get ground up by the teeth of the starter ing gear as it whizzes around and eventually the remains will get spat out of the slot. It is highly unlikely it will do any kind of damage at all.
Obviously it's best not to push anything into the bell housing and you certainly don't want to poke anything in there when the engine is running but the chances of a bit of rubber doing anything bad are very slim.
Buy a new one, instal it and never touch it again. It has no purpose on these later bikes so there is no need to take it out. Some people pop it out to pry the non running motor around to find TDC when doing the valves but since the CARC bikes have an easily accessed nut on the front of the crank for that purpose there is really no need.