"The term Brit means, to me, English, Scots and Welsh with Irish thrown in depending on the discussion and on whether any Irish are within earshot"

As far as that part of Ireland that is part of the UK goes I'd imagine you'd be just as likely, or arguably more likely, to get yourself into hot water if you suggested that they weren't British. I wouldn't fancy going to watch Northern Ireland play football, or go to a pub on the Shankhill, and tell the people "Nah you guys are not British!"

Suicide mission springs to mind!