It is certainly a possibility.
I have always had major doubts about the EU - no, I am not anti-immigrants or a racist, blah, blah, blah. I should not have to say this, but it is necessary in the current climate.
Right at the beginning when we voted on the Common Market, I was concerned about what the future held. About creating a "playground clique". About the inevitable tortuous nature of decision-making in such a large organisation. About how we might come to think about those who were not "in" - if some are "in" then some will be "out" by definition. About the danger of creating another block of countries vying for power in the world. About the possibility of expansionist aims creeping in. About the inevitability of a few countries within the group taking precedence and their wishes being foisted on others. About it becoming a focus for general discontent (as it has) and how this might play out.
I could go on. None of my concerns were about not wanting to get on with our European neighbours; but about the fact that the worst violence and discord happens within families rather than with neighbours.
It only takes one thing - a global recession and its ensuing discontent in this case - to start a backlash, and the EU officials are giving us a hard time because they can see that we might not be alone in our concerns.
There has not been a major European war since the 2nd WW and there are those who conclude that the EU is the reason for that. But it is always wrong to assume a causal relationship without proof.
My concern is that countries who wish to extricate themselves will lean towards the far right - we have seen this at home. The EU needs to think how it operates if it wishes to keep its members on board and not find countries leaving and being cut loose to sink under some far right intolerant regime.