Well yes, that's because it is part of the United Kingdom. So it is right that it does.
The problems will arise if and when there is a UI. Presumably the UK will back out and have nothing more to do with NI, so it will be up to ROI and NI to fund it going forward. There may be a transition period where all countries contribute but who the heck knows!
So then we have Ireland which is racing ahead of all parameters in the areas of the economy, education, high tech, pharmaceuticals and so on. Its tax take is largely dependent on foreign direct investment companies and being a member of the EU is advantageous for sure.
There will be a huge drain in taking on a NI that is barely surviving, where the bigotry and low level terrorism is just under the surface ready to break out like a tinder box, where the majority of employment is in the Public Sector, and NI is not formally a member of the EU. What will it contribute to a UI? I mean seriously, I don't think people with their rose tinted glasses on can see beyond a 32 county Republic. I also think that there is far too much going on in the world to initiate a UI right now. Eventually it will happen I have no doubt about that, but the timing is not right just now, it will open up some wounds that have barely closed and all hell might break loose again. I don't want that, and I doubt many others do either.
It's a big question, but definitely one to watch!