How would Americans speak differently if it was a peaceful part of the Commonwealth? What would be the primary dialect? What dialects would most likely disappear?
I too don't think US English varieties would sound too much different to what they do now. However, I wonder whether the elite might be more British sounding? I wonder whether you might get a "Morningside" US English, i.e. a variety of US English that developed from trying to sound more British but ends up as a unique form. (Morningside is a posh area of Edinburgh). I wonder too whether this Britticised elite might use more British/English idioms.