I'd wager against that. Seriously, the worst of the EU is too wimpy to even fight. The can't we all get along mentality of the Scandanavian nations is spectacular.
I think the EU might collapse, but it won't be for military reasons.
They'll fight. They won't fight people they don't know who threaten they're lives but they'll frag their neighbors in a heartbeat.
Remember: Leftists are only pretending to be good people. The farther left they are, the more rage lurks inside them.