Should the EU prepare for a large influx of American and Canadian immigrants?

So, with the current state of affairs on the North American continent, chances are that things will get out of hand and society falls to violence.

This would cause a large group of Americans and possibly Canadians to want to get out and go to Europe (assuming they would prefer Europe to other options).

The EU has a lot of problems with aging populations and not enough births. Assuming a lot of the US people are young, pretty well educated and culturally compatible, should the EU be welcoming these people? Maybe even advertise the EU is willing to receive Americans and Canadians if they want to leave?

Right now, immigration laws in the EU are strict (though varying per country). Do you think we could and should make extra provisions for a possible influx of American 'refugees'?