if they get admitted as a state they'll get american gibs. same as canadia.  it feels like most of this is about russia. both canada and greenland are just across the arctic from russia and it feels like the drive to consolidate them directly into america would only be motivated by a desire to tighten up that border. canada is already something of a subjugated state so the only reason to formalize american dominance over them would be to make cooperation smoother, like you might need for wartime.
United States