Reading your last post, I would mention that I had found a cite mentionning the birthrate of Morroco, Algeria, Tunisia, Turkey, etc but didn’t post it because I couldn’t translate the birthrate into a number of child per couple. In any case, Algeria had the second highest one behind Lybia. Now, given your comment, maybe it isn’t true anymore since I don’t remember the date of the study.
Anyway, it seems unlikely that migrants would have significantly more children in their country of destination than in their country of origin (that’s why I originally considered posting these datas).
Aye, there’s the crux of the biscuit: Europe will be all you say she can be and more if she can streamline her markets.
But I think overcoming 100% of the nationalistic-type issues is going to take more like 100 years than 15; I just have a hard time thinking that Poland is going to have no problem with letting German troops across their border, or that the UK will happily put all their forces under the command of a continental general.
And making Europe’s economies dynamic is still going to involve the political will to take away power from the unions and the workers in order to make businesses internationally competitive and encourage entrepreneurialism (Or else, as my selfish preference would be, to get the US to adopt more EU-like regulations. 35 hour workweeks for everyone! 
). Especially as India and China and the rest of Asia develop, the global marketplace will punish uncompetitive companies. As you point out, Europe produces perfectly good innovators; the question is, can they create a business environement where it is their interest to stay, and indeed where more and more are coming to the EU from the rest of the world.
There’s no reason the EU can’t do all that. There’s no fundamental reason they can’t slash spending and triple the defense budget … but I think it would take an event bigger than 9/11, or some sort of economic collapse, to create the political environment where they want to. Since I don’t see (or want) either happening anytime soon, I can’t see the trends changing.