Given my country isn't part of NATO - not really.
I think it'd be stupid for the US to do this. On the other hand i would kind of welcome it, because it would make a defensive pact within the EU necessary, which in turn would be an important steps towards united nations of europe - i hope i live to see the day.
Indeed i have. While the Austro-Hungarian Empire was able to integrate the czech and hungarian parts reasonably well (though it took way to long) - one of the reasons it ended was that they weren't willing to give the Balkans the same rights. The empire didn't crash because it was too big or there were to many different people. It treated its people differently and ultimately broke down - so lessons to learn: treat people equally.
(though you can also argue that the beginning of the end was with the rise of Prussia and 1866, it just needed a trigger)
Integrate the Czechs well? Oh so that is why my ancestors had to fight for generations to get even basic rights. And in the end despite all the struggle, the monarchy was unwilling to give them the same status as the one the Germans had. As for Hungarians, they only stopped causing problems when they achieved near independence.
And Austria-Hungary fell apart because apart from Germans, everybody else was forced to be a part of it. As soon as it lost the ability to force everybody to stay in, it disintegrated. Oh and fun fact: The empire had a lot of German, Hungarian, Czech, etc. citizens, but no Austrians, just like the EU.
If idiotic politicians force though United states of Europe, they will fall apart during the first serious crisis.