There's pros and cons to that. Some of the cons could be (not always, but definitely sometimes) the creation of parallel societies, high unemployment and crime rate and a possible decline of the welfare state (due to people not wanting to pay a lot of taxes to support people who are less "like them"). Success depends a lot on the host society, on the immigrants themselves and the values they grew up with and a whole bunch of other factors. And in general in times of economic hardships (which we are very fast heading into) it's hard to assimilate immigrants.

Also we need to talk about volume and skills - the current Ukrianian diaspora in the EU is highly skilled, young and relatively small. What happens when you inject millions more (Ukraine has a population of 40+ million) including the elderly and the unskilled? It's a different ballgame.

I think the best we can hope for is for the situation there to relax and for the poor Ukranians to be able to live peacefully in their home country. For most people - living in a foreign country is hard and not a blessing.