Personally, I would say no. Ireland is rich in the renewable resources of the post-carbon era: wind, wave, tide, solar, biomass. Also, nuclear power in Ireland would simply not be economically viable without considerable state subsidies. I would assume that bankrolling such government subsidies is not what the carbon tax was intended for.
However, debate on the topic is essential and the following articles make for a fascinating read:
Head2Head - Does Ireland need nuclear power?
Sound points are made by both sides, but I leave you with the words of Oisín Coghlan. He says no:
And let us not forget that no country has yet developed a repository for the long-term storage of the high-level radioactive waste. Waste that has to be kept safe, without leaks, for over 200,000 years, twice as long as homo sapiens have been on Earth.