There is no chance 1.2B people will migrate to Europe.
The problem is that, right now, EU countries are forced to accept poor immigrants and integration is not easy.
Integration is not easy for a number of economical reasons and not due to xenophobia. EU economies, especially in the south, are not doing well. There are not a lot of jobs, life got progressively worse in the last 20 years, crisis after crisis.
So naturally, migrants will end up working for 2€ per hour picking up tomatoes or selling drugs and stealing bikes.
Eventually, it will become politically unsustainable and local populations will vote to quit the EU and stop the immigrants flow.
The nordic countries have a rape problem linked to immigration. My grandma is afraid of walking in her own city. I'd say we're about 50% there.
We already saw it happen in the UK. The only thing keeping the other countries in is that their economy are too weak to survive on their own and they came to rely on the single market.