Transferring the crew is allowed, but all of the extra effects caused by it will cease as soon as the possessed crew is separated from the possession source. It will revert back to its original nationality, it will take up cargo space again, and its point cost will apply normally. (ADDED: It does not return to its original owner.)
The same happens if the Possession ability is cancelled, except in that case you may end up having to eject some crew.
For clarification, this applies to the ability of Wraith (SS) and Captain Davy Jones as well, and not just to the “possession” ability of Papa Doc?
Devil’s Maw is one of the only things in the game that will permanently alter a crew, and that’s mostly just because of the way that crew (don’t) interact with forts.