Won't happen.
The IFA won't even apply to UEFA (as they have been repeatedly invited to do so) for dispensation to allow Norn Iron citizens with Irish Passports to play for them.
Never mind that it is the democratic right of any citizen of the Six Counties to hold an Irish passport "without prejudice or recrimination of any sort", according to the Good Friday Agreement. They prefer to feign indignance and enjoy a good whinge when Nationalist players decide they don't want a British passport, thanks all the same, and opt for an Irish one. Effectively, they've given any Nationalist player in the Six Counties a choice: renounce your heritage or you won't get capped. Stunning ignorance when you consider that Nationalists make up between 45 and 50% of the population.
The FAI was formed as a reaction to this sort of small-mindedness, almost a hundred years ago. Lord knows, it's a f**k up of an organisation too but, in their defence, they have no truck with that sort of shite. They're just incompetent.
Derek Dougan organised a one off all-Ireland team (under the guise of a Shamrock Rover XI), back in the Seventies and was ostracised by the IFA afterwards. The FAI did nothing to support him afterwards either.
The other major problem is that the bigwigs of both organisations both like being a big fish in a small pond. I imagine that only if UEFA ever force the four Home Nations to merge, will we ever see the Norn Iron football fraternity assert its kinship with their Southern cousins. Rather like their farmers were at pains to declare their Irishness when British beef was banned due to the Mad Cow Disease scandal.
Mad Cow Disease... f**k me, it'd be easier cure that than some of the shite and bitterness that eats away at the citizens of this island.
(Irony of that last sentence sadly noted, before anyone collars me on it).