According to Revenue
"If you reside temporarily in the State primarily for the purpose of pursuing a course of studies you may bring a foreign registered Category A vehicle (e.g. a saloon, estate, hatchback, convertible, coupé, MPV, Jeep, etc. a minibus (with less than 13 permanently fitted seats including the driver's seat)) or a motor-cycle into the State provided it is registered in the country of your normal residence. The same conditions mentioned in paragraph 2 above apply and the 12 month time limit will be extended until you have completed your course of studies."
I'm not sure how they would go about getting an MOT every year - apart from maybe driving over the border to get one?
The UK insurance may be a problem too with an Irish address and Irish companies probably won't insure a UK reg car. (Quinn seem to be less fussy about Uk/Irish addresses.)
Also - UK car tax would need renewing every year ? Not sure how that would work?