Whether you would or not is irrelevant.
Fact is, St Patrick's Day is Northern Ireland's Saint's Day. It is also the Republic of Ireland's Saint's Day in addition to Nigeria and Monserrat.
That it's not exclusive to Northern Ireland doesn't prevent it being Northern Ireland's Saint's Day.
Would you argue St Andrew's Day isn't Scotland's Saint's Day?
After all, Romania, Russia, Greece and Ukraine amongst others also have it.
As it is, I've been developing my own specific symbols and baking for St Patrick's Day that doesn't fit the stereotype of green, leprechauns and all that. It's centred around Northern Ireland and symbols, e.g., hexagons for Giants Causeway.