Yes, the UK leaving the EU will ultimately cause the EU to unravel. The UK is one of the most important and needed countries in the EU, and both the UK and the EU will have lots of problems after they secede. Brexit, the British exit from the EU, will impact the entire world's economy for years.
The vote for the U.K. to leave the European Union was a historical one indeed and something that nobody really saw coming. The world really does seem to be unraveling and we are definitely living in unpredictable and tumultuous times. Who knows what the future will hold now. We may not be a world united but instead a world divided where every country fends for themselves without any help from anybody else.
In the weeks leading up to the controversial "Brexit" vote, there was speculation about whether or not the U.K.'s leaving the European Union would make an impact. It definitely has: now that the U.K. has voted to leave the EU, the value of the pound has collapsed and borders are becoming more strained. It's only a matter of time before the EU descends into infighting and other countries decide to leave as well.
There are those members of the EU that have and will continue to benefit from their membership in the union. Those countries will certainly look at how their separation from the EU could potentially affect their countries, economy, politics, foreign policies, and ultimately their nationals. Those countries would remain loyal to the union.