No, EU enlargement will not result in destabilizing job migrations, because job migrations are not necessarily destabilizing. Expanding the EU makes it easier for people who need jobs to move to places where jobs exist. A person who moves for a new job is not destabilized, they are more stable. This is true on an aggregate basis.
I believe that at any time a country's overall size increases there will be some sort of economic and political distortions from a statistical standpoint. Job migration will fluctuate based on growth and decline and if the EU increases in size or decreases this will have an effect on the stability of labor force migration.