That is a legal gray area. If South Viet Nam ceased to exist, then so did North Viet Nam. If the reunified country, whoever it is, is legally or even morally obligated to honor any sort of gentleman's agreement or legal treaty from one of the previously existing side, the reunified country is equally obligated to honor the same from the other previously existing side. So if South Viet Nam was the administrator of the islands as recognized by other countries and even by North Viet Nam, the reunified Viet Nam can argue that the islands belongs to Viet Nam, or at least demand international arbitration.