Are you sure?
They told me over the phone that the only way to add the "gold club" into the reservation would be to cancel the reservation and re-book. The problem with doing that, as they explained, is that the booking is done through a Delta voucher, and once they cancel the reservation (in order to re-book), they will lose the voucher in the system.
I guess I won't know until I am standing at the counter, huh?