I wonder if it might work differently depending on how long the card had been registered, and/or how many cards you'll have left (after auto-deleting).

The RN system won't easily let you delete (unregister) the last card from a particular RN program. You always need to leave one card there. (It doesn't have to be a current card, it can be an expired card, since they only check the number, not the expiration date, when you register.)

In all the cases where I've moved cards just by registering at the "new" program (without manually unregistering at the old program), it's been at least a couple months since I'd registered that card in the other program. (And I'm leaving a few cards in the old program in most cases.)