Not necessarily. Such an event would be a geopolitical reenactment of the Danish folk tale "The Emperor's New Clothes". Turns out the emperor isn't just naked he's still living in his parent's basement. And the emperor here is Europe and the parents are the US. Why would I as a German support a war over an island that has not just been criminally neglected by a supposed alley (Denmark), it is even politically and economically irrelevant (as of now). And not just that ... "we" have been begging the US to keep protecting us and for them Greenland is in that respect very much serving a purpose in line with that very military support. Europe is naked as it stands. I don't like it. But that's just how it is.