I'd just like to point out that mitochondrial DNA is evidence only of descent from the mothers, which does not preclude, for example, invasions of 'Celt' warriors, raping as they went. If every aboriginal, non-Celt Irish male had been killed and all the women impregnated by Celts, the mtDNA would still not show any Celt influence. (I'm not proposing that this is what happened, just pointing out that there are limits as to what may be inferred from mtDNA).

Another issue is that Celt is now generally not held to have been an ethnic designation, but one of language, material culture and myth, which are things that would not necessarily show up in mtDNA. So McEvoy and Bradley's findings, while very interesting, are not really apropos. The apparent fact that the matrilineal ancestors of Ireland came up from the Iberian peninsula after the last Ice Age does not mean that Ireland was never a heavily Celtic culture. A parallel example might be Roman Gaul- what is now France was eventually 'Romanized' in terms of language, architecture, material culture and political structures, but genetically the population were not all Romans.

By the way, here is the home page of the authors of the study quoted by the OP.
http://www.gen.tcd.ie/molpopgen/index.php