I don't think it will make a difference. There's always been smuggling between the two. Unless they build a wall - which they won't. Remember the old cow trick. They'd cross UK cows over the border - claim EU subsidy - then walk them back and repeat a month later.

Anyway, despite what they say, the word in the inner circle in Brussels is they will agree a trade deal quickly as it's in their interest despite the rhetoric, as of course they are desperate for the UK not to leave the EU.