I doubt it. We will probably destroy ourselves by more conventional means before technology gets to that level. It would be nice to think that wars could be won without killing people, but the robots would probably be directed to destroy the opposite side's programmers. If such a thing did happen USA would have an advantage because we have a huge army of teenagers who play video games.
I don't think so. Slapping a pistol in a conscript's hand and flinging him out into the middle of hell on earth to die on your behalf will always be cheaper. It comes down to the cost. In the eyes of any government, citizens are plentiful, a steady flow of cash is not.
It would be fun to watch robots get owned. Then again, I don't see it happening, technology hasn't reached that stage yet, nor will it reach the stage of robots we can trust with weapons. They'd probably end up destroying the human race!