That's something I've been trying to get my own head around and was mulling over the various possibilities a few pages back, but I can't say anything for certain. It's the reason I didn't go into article 17 - or what tends to be known as the "granny rule" - in my piece as I would only have been basing my arguments on conjecture. Likewise, I avoided the questions surrounding the eligibility of the likes of Adam Barton and Alex Bruce, because their circumstances are slightly different to those born in the north and I'd only be speculating as to which article they qualify under. I've sent an e-mail to the FAI's legal head though on these issues, so I'm hopeful I'll get some sort of response to clear this up.
What I know is that hypothetical player B would be entitled to Irish citizenship so long as it had been passed onto him via descent, or registration with the Foreign Births Register. The parent (player A) or grand-parent through whom it would be passed would also have had to have been an Irish citizen at the time of this player B's birth. Whether that would make him eligible to play for Ireland or not is another matter.
There's more information on the citizenship side of matters here:
http://www.citizensinformation.ie/en...r_descent.html
What I've been wondering is whether player B would be deemed by FIFA to be a permanent Irish national or whether he'd be deemed to be acquiring a new nationality and, therefore, be obliged satisfy the criteria laid out in article 17. If he'd have to satisfy article 17, I don't see how he'd qualify as neither he, a parent or a grand-parent would have been born in the territory of the FAI. If however, his citizenship was construed to be formal and legal recognition of his permanent Irish nationality, he might not be deemed to be acquiring a new nationality after all and might actually satisfy the general principle laid out in article 15, thereby making him eligible to play for us.
The reason I think article 15 may apply in such instances is because, if interpreted literally, article 17 would surely disqualify the likes of Barton and Bruce. I acknowledge they would be categorised as player As under your example, but I'll explain why they're relevant to working out the article under which Irish nationals via descent might qualify. Defining NI as the territory of the FAI would appear to be a stretch of meaning and would certainly be a contentious interpretation, no matter what our own political views on the matter would be. Indeed, if article 17 did disqualify the likes of Barton or Bruce, but they are still perfectly eligible to play for us, then it would have to be article 15 under which they qualify. Essentially, what I'm saying is that maybe article 17 isn't the "granny rule"; maybe article 15 has that effect and so even those who are Irish via descent beyond an Irish grand-parent may well be perfectly eligible to play for us just so long as they are permanent Irish nationals, independent of any residence in Ireland.
Out of interest, did Chris Hughton qualify via an Irish parent or an Irish grand-parent, because I know his son Cian is eligible to play for us? I think Chris might have had an Irish parent, mind, but maybe someone could clear that up. Once again, though, the above is just my own speculation and guesswork based on how I'd interpret the text in light of the reality that Barton and Bruce do qualify for us. In spite of what some might have said, I'm certainly no authority. :p