No, they certainly wouldn't, but in the realpolitik of war, they would provide the justification for the USA to engage in an armed response to retain the territory. Basically think of the two scenarios of what would happen in the Falklands in 1982 if either:

a) the islands were claimed by the UK but also completely unpopulated and were occupied by Argentina

or

b) what actually happened, the islands were occupied by almost entirely UK-descent, English speaking subjects of the Crown, resulting in subsequent military action that had broad and overwhelming public support in the UK.