It's a tough call. The fact that all-local production ended would go against it, as would the fact that lots of non-Irish breweries make something they call Irish dry stout. Then even in Ireland, recipes vary hugely: if you were just going to say "Irish stout = pale malt + roast barley", you could make a case. But that would exclude lots of Irish stouts, like O'Hara's, from calling themselves that.
And probably the biggest kicker is, as you say, the Big Two are likely to have as much claim to any designation as the micros.