It would, but it would not be entirely implausible in this case. Greenland has self-rule on internal matters, but foreign policy and defence costs Denmark money. It implicitly accepted Greenland is headed for eventual independence, but it needs to be economically viable first. If Greenland turns down revenue from mining and in doing so drives up defence costs for Denmark, it's not inconceivable some people will decide they can't have it both ways.

That said, I don't think it's likely.