If someone from, say, Roshar, traveled to the world of Warbreaker, do they have Breath?
No, they do not. And if someone from the Warbreaker world leaves, they will still have their Breath... They would not register as being a Drab to people who are looking. They would register as Option C. Particularly someone from Roshar, who is from a primary Shardworld, is slightly Invested.