It absolutely could... but a major promise of the Brexit campaign was to "secure their borders" so that's a no-go. Plus it'd result in a hell of a lot of smuggling into the UK, and they'd be sanctioned under WTO rules since they'd be "favouring" Irish products and discriminating against others. For example US apples that came into a British port would have to pay tariffs while Irish apples driven across the border wouldn't, which is a big no-no under WTO rules where the first and foremost rule is that you must treat countries the same using WTO rules. So they'd be forced to either drop checks everywhere, or to erect them at the Irish border, or to do this legally they'd need a separate Trade Deal with Ireland, that is with the EU... which puts them right back at square one.