The Prince was flying an ASW helicopter from Invincible, which per standard doctrine never went near any enemy combatants itself. So for him to be captured he would have to have been shot down, presumably not by a submarine, survived and been rescued. It is vaguely possible I suppose but a stretch, it's not like we were using Sea Kings to bomb Stanley. For him to have been killed, most likely by mechanical malfunction rather than enemy action, is far more plausible, but apart from family grief and national shock the implications would have been small, maybe greater and longer-lasting resentment against Argentine aggression which led to this and so many more tragedies.
Had he somehow been captured the consequences would have been less I would say. The Argentines would have been expected to treat him honourably, and I imagine would, and hand him back promptly on conclusion of hostilities, if not before that on parole. If they did try to bargain using him they wouldn't have had much of a hand, we after all had thousands of prisoners, not one however important, and international reaction would have been very negative I would think.
PS isn't this on the wrong board? I have the impression that 1982 was definitely after 1900.