The whole thing would be plain stupid, how do you distinguish one worker from another and what chance a surge of EU people suddenly arriving just before the vote which would no doubt have Daily Mail readers frothing at the mouth.
Opposite our offices is Santander UK headquarters where around 40% of the staff are Spanish, the floor below us that company has around 25% of French people. I would imagine a good 10% of my company are EU nationals so this could be a serious issue around skills required by UK Companies.