I don't think that there ever will be a EU 'national' team - despite my belief that some day it will be a 'nation'. In time, there will be super-powers football-wise, which aren't particularly good now - USA, China, Japan, Cameroon, Nigeria, etc, but the European nations will be left behind. Despite this, there won't be a EU team for one reason: we've never had it before.
Many countries' national teams continue for the purpose of beating another country. The Scotland team will never win the World Cup, it's pretty safe to say, but they take enormous (and I mean ENORMOUS) pleasure when they beat (or draw against) England. I'm sure that this is the case with many 'lesser' teams. Maybe the Belgium team exists to pour scorn upon the Dutch. Maybe the Portuguese love to better than Spanish. Whatever the rivalries around Europe, I can't see an overnight change between national teams in continental teams.
Say it were to happen after the World Cup, and the European team choices Figo and Raul. Spain have just beaten Portugal 6-0 in the World Cup Final, with Raul and Morientes grabbing 3-a-piece. I don't think that Figo and Raul will feel like team mates, and I'm pretty sure that they won't play to their full potentials, so it won't happen.