One of the question that I posted an answer to got migrated to another SE site (from ELU to ELL). My username is grayed-out under my answer.
My question is what happens if someone upvotes/downvotes my answer? Do I gain/lose rep?
Once you create the account on the target site, all the votes you've got while having your name grey (and also the votes you received before the question was migrated) are associated with your account and you immediately get (or lose) the rep for them. But not until you create the account - because there's nothing to assign the rep for.