The ways of democracy are strange. When Iranians voted 98% in favour of creating an Islamic Republic, and North Korea supported their regime by a similar proportion, nations such as the USA have not exactly supported the overwhelming voice of those peoples. The same will almost certainly be true for the Falklands, where the USA remains firmly on the fence. Argentina has already stated it will not recognise the referendum.
I am sure it will be conducted openly and constitutionally, with international observers, but in the likely event of a massive vote for UK alignment nothing much will change other than there will be a verified article of expression rather than just surveys.