uh, as far as i understand it, the EU itself cannot go to war anyway as it is primarily an economic agreement, right? is the EU leadership elected by the people, or appointed by the states?
there was supposed to be a common EU defence policy and an EU rapid reaction force, but it hasen't happened yet. It was mostly a German and French wet dream, the rest aren't that interested.
The EU comission is is selected by governments, only the EU parliament is elected by the people. The comission has more hands on power in the day to day leadership of the EU. So, it's hardly a democracy.
The parliament though can fire the comission through a vote of no confidence, and has done so in the past during the corruption scandals.