1: Although there would be migration, the islands would inevitably want to prevent a flood of people to prevent a plague outbreak on the island itself, so they would try to restrict immigration to the best of their abilities.
2: I opened a can of worms here, didn't I? Regardless of which people managed to get across, I'm just noting that there would be immigration, and it most likely wouldn't involve a million peasants sitting in refugee camps. I'd imagine that it would involve kings, theologians, inventors, merchants, and other high-ranking individuals from throughout the continent fleeing and reestablishing a new life. Whether or not a mass immigration would involve the poor, this would be a new batch of labor and capital into the islands. We could reasonably increase the base tax, or place a couple buildings, to account for this change.