I guess that a major war amidst Europe would actually work against Argentina
If I got your point correct, of course. You seem to imply that when (if) a war starts in Europe in which GB is going to participate, it will lose all interest toward their overseas territories, right? And then Argentina could easily capture the Falklands, as you seem to assume. In reality, though, if anything such is going to happen, Britain will just nuke Argentina back into Stone Age without much ado, and it will quickly forget about the islands for the next few centuries (if not millenia)
If there is a major war in Europe, and the United Kingdom is one of the participating nations, then Argentina can easily get support from the other side.
Suppose if the war is between the UK and Germany, then Argentina can strike a deal with Germany. In this deal, the Argentines will provide military help and food exports to Germany in exchange for the Germans providing air defense for Argentina
You must be kidding mate!
Do you think that Argentina becoming an ally of Germany will somehow save it from nuking? I guess that would actually make it into a primary target. GB will never nuke Germany, no matter how things are going to evolve (since that would most likely lead to an escalation up to a full-fledged exchange of nuclear strikes across the world). Instead, they will just nuke Argentina (Falklands or no Falklands), and no one will give a fuck about poor Argentina. Germany will most certainly seek help from Russia, and you can pretty soon expect Russian "peacekeepers" to be deployed near la Manche. And the war will be over in two weeks (with Putin declared as the emperor of a new Holy Roman Empire, from ocean to ocean). The US most likely won't interfere (as per usual in any serious skirmish)