Two recent decisions by European official bodies indicate that the answer to the question posed in the title of this article may be "yes".
The court of the European Union has ruled that no member country has the right to close its borders to illegal immigrants if doing that is contrary to EU policy. I can't think of anything the court could have done that would be more likely to trigger more withdrawals from the Union.
Every member country knew that by joining the EU it would be giving up part of its sovereignty, but the primordial duty of any government is to protect the state and its citizens, and if a member country is denied the fulfillment of that duty it will have no choice but to refuse to accept that ruling, and if necessary, withdraw from the Union. Poland and Hungary have already declared that they will not recognize the ruling and it remains to be seen if other countries will follow suit and, if they do, what the bureaucrats in Brussels will do about it.