That would actually be a very good solution to the problem of how to preserve the stealth aspect of privateer raiding. However, I share you pessimism on this... More likely they will just reuse the "gift unit to city state" functionality and have the captured ship disappear and then reappear in the capturer's capital a few turns later (explained as "price crew sails it home"). That way you couldn't be sure whether the capturing civ stole the ship or built it. It's not as elegant as that "jolly roger fleet" idea of yours, though.
Of course, the worst implementation, and unfortunately also the easiest, would be to simply have the captured ship revert to its new owner immediately and thus giving away the privateer's nationality. Hope it's not this...