If you had a dismembered USA where all the colonies strike out on their own, its plausable one or more might take the Prussian route to secure their possessions but otherwise it is unlikely. An army has to justify its existance. There is no real justification available for OTL USA.
I could see something sorta like this...
Britain retains control of the Carolinas, Georgia, and the west at the Peace of Paris. This is fairly plausible, I think. Jefferson, alas, is shot during a raid on Williamsburg, or something.
So, the Constitution is even more centralized than OTL. And during the French Revolution, Hamilton decides to take advantage of the situation to take control of the Midwest, while Georgia rises up as well. It works, but, America's been... rather altered.