I was in a very similar situation and it didn't prevent me from getting it.The Irish consulate accepted my grandmother having been born in Ireland after having been given a copy of her marriage certificate and death certificate...both or which listed her birthplace as "Ireland".If,by chance,you wish to pursue the matter I'd suggest that you give it a try.You just might be able to do it...particularly if Irish authorities haven't changed their policy since I made my application.
Thanks. My world-traveling daughter says she would LOVE to have an Irish passport. Says it saves tons of time traveling around Europe. I’m gonna try your idea and see how far that gets me.