Since the purpose of "plumber's tape" (which is actually a very thin gauge ribbon of Teflon plastic) is to fit within the spaces in a standard threaded joint, it stands to reason that using it for a cork makeup device would both require a lot of it, and would involve movement of the successive layers against each other as much as it would allow the mouthpiece to do the same thing.
A better "emergency repair" item would be either vinyl tape or medical tape.
I carry a couple of rolls of clear hockey tape (used to tape up socks and the like by hockey players) in our "gig bag" (a duffel bag that goes to all band jobs) for stuff like this. It's easy to cut, stretches slightly, and adheres very well to itself, and works well for everything from taping up a wire connection for the sound system to building up a dying mouthpiece cork.
The other alternative is a lot more costly, but has more "give" to it in compression terms. This tape replaces the old adhesive tape used to build up custom sized bandages. Again, it's easy to manage, and cleans up well in the bargain.
Push comes to shove, there are few problems in the world that cannot be patched up by enough hockey tape. Oddly enough, I don't use it when I play hockey, but have found dozens of uses for it with everything else.
One caveat there, however. It is not electrical tape, despite how much it may look and act like it.