I don't think it's really that unlikely that someone from Armagh would identify as Irish over Northern Irish or British (stats say that 50% do) and we all play to our stereotypes when we are in unfamiliar places.You're welcome to do what you want man, but hoo boy you have no idea how much worse you just made it. Northern Ireland is a different country. One where border tensions have been extremely bad for a very, very long time.
At the end of the day, do what you want, I just felt I had to say what I had to say.
For comparison though, imagine the character is supposedly from Texas, speaks with a Boston accent, and you've just said they're from "Up near Ottawa".
From my experience of living in my little den of republican sedition in the 2000's I can assure you that none of the folk from NI that I know consider themselves British and are very much capable of acting like they're from Gallway and smashing out some Gaelic when they're "on the mainland" (that phrase would really piss them off).
I would also suggest that in Molly's lifetime border tensions have hardly been "extremely bad".