Yes, but does UK citizenship / resident-alien status / locality have anything to do with eligibility for .ie TLD registration?
The description of who can use *.ie is slightly vague on Wikipedia, but indicates there has to be a "tie" to Ireland. Moving the company out of the country seems like it might break whatever tie was there if it's based on any of the above criteria.
It's already too complicated to me as an Ugly American to differentiate Ireland, Northern Ireland, the UK, (Great) Britain and/or England, I'm hoping someone with more expertise can comment.
Ireland and Great Britain are islands. On these two islands are two sovereign states: Ireland and the United Kingdom of Great Britain and Northern Ireland (also known as UK). The UK consists of four parts: England, Wales and Scotland on the island of Great Britain and Northern Ireland on the island of Ireland.
.ie is the domain of the state Ireland.
.uk is the domain of the UK.
Ireland is not part of the UK, but it is part of Britain.
Northern Ireland is part of the UK, but that's a completely different country from Ireland. Being UK born or based gives you no privileges over the .ie domain at all.