There's been lots of talk that this won't happen but it's hard to see how there won't be at least some sort of checks reintroduced. This isn't too unusual, we had the Common Travel Area[2] since 20s well before Schengen but a return to any sort of militarized or "formal" border could easily kick it all off again in the border counties.
For an idea of the difficulty here's what crossing the border looks like the BBC did a little drone video where it's very easy to see how "leaky" it would be [3]. When I was growing up it looked more like this for the main routes [4].
[1] https://www.youtube.com/watch?v=xz35L-TBt9M
[2] https://en.wikipedia.org/wiki/Common_Travel_Area
[3] http://www.bbc.co.uk/news/av/uk-northern-ireland-40104333/cr...
[4] https://i.pinimg.com/736x/23/a3/54/23a354665613f3aa695f0e5c3...