Yes, it will survive. It must! Europeans needs to understand that extremism cannot win. A Europe without EU will certainly be more opened to conflict between countries. Let's not forget why EU was created, to confine extreme nationalism which had devastated the continent in WWII. Now it's easy to forget that another world war is very possible to appear.
EU is not only about who can buy more bread or milk.
There are voices who say that eastern countries should be out of UE. Would you rather see these countries stand for what Russia stands for?