More than that, the whole Irish double Dutch sandwich with extra ketchup bullshit won't apply any more.
Sure it will.
I realise lots of people really don't like the "Irish double Dutch sandwich with extra ketchup bullshit" strategy, but there's no reason at all why this won't work afterwards. Arguably, it'll work even better than it does now.
The only difference is that we could substitute ourselves for any part of that arrangement, knocking Ireland or Holland out of contention. Or both, if we chose. I'm not suggesting we should, simply explainin that we could.