No it should not start the game with such a core, because we do not want the Teutonic Order to declare a war on Sweden or Denmark and try to conquer Gotland when it historically did not do that from 1419- 1820
What I could see would be if you make an event for LAT under heavy conditions about Gotland and only in the ahistorical b choice give the player a claimcore on the island.
I second that. No core at start and prehaps a "reclaim kustrin-esque" event that fires when LAT or TEU control Gotland.