Even in the worst case scenario, that decadent Europe will be totally overrun by the Muslims (and it seems conceivable), I don't see a viable society with them. They'll be too busy killing each other to tend to government, social services, etc. Basically Europe would just revert to the Dark Ages, as it did after the fall of Rome.
Bin Laden is truly living in a fantasy world. He keeps hoping the Islamic world will somehow restore all the former glory of 8th century Baghdad. Even that was a myth. The corruption, cruelty, & perversion there was rife.
Islam thrived among small, self-contained tribes. There is no unity among them.
You are right. Somehow, I can't see them coming up with the next generation of BMWs, or a new Airbus.
Without the Europeans to live off of, they do not have an economically viable way of living in Europe. The ones there are completely removed even from subsistence farming and small-time trading.