Based on Irish law, specifically the Irish Nationality and Citizenship Act 1956, can I live abroad after naturalizing as an Irish citizen and retain my citizenship just by filling that form?
Yes, subject of course to factual disputes. The statute provides that this revocation is not possible when the citizen has "registered annually in the prescribed manner his name and a declaration of his intention to retain Irish citizenship with an Irish diplomatic mission or consular office or with the Minister":
Revocation of certificates of naturalisation.
19.—(1) The Minister may revoke a certificate of naturalisation if he is satisfied—
(a) that the issue of the certificate was procured by fraud, misrepresentation whether innocent or fraudulent, or concealment of material facts or circumstances, or
(b) that the person to whom it was granted has, by any overt act, shown himself to have failed in his duty of fidelity to the nation and loyalty to the State, or
(c) that (except in the case of a certificate of naturalisation which is issued to a person of Irish descent or associations) the person to whom it is granted has been ordinarily resident outside the State or, in the case of an application for a certificate of naturalisation granted under section 15A, resident outside the island of Ireland (otherwise than in the public service) for a continuous period of seven years and without reasonable excuse has not during that period registered annually in the prescribed manner his name and a declaration of his intention to retain Irish citizenship with an Irish diplomatic mission or consular office or with the Minister, or
(d) that the person to whom it is granted is also, under the law of a country at war with the State, a citizen of that country, or
(e) that the person to whom it is granted has by any voluntary act, other than marriage or entry into a civil partnership, acquired another citizenship.
To be precise, filing this declaration does not protect the citizen from revocation of naturalization under another subsection of section 19(1). But if we assume that the annual declarations were all filed promptly (or that there is a reasonable excuse for any failure to file promptly), and that there is no dispute about this, then it is plain from the statutory text that the minister has no discretion to revoke the certificate of naturalization under 19(1)(c).
If it were a country like UK or New Zealand, it would straightaway revoke citizenship by claiming misrepresentation of the intention to reside.
This is not necessarily true. If there is a reason for the decision to leave, the naturalized citizen could seek to rebut any presumption that there had been misrepresentation.
In the case of Ireland, filing the annual declaration does not protect the naturalized citizen from denaturalization under 19(1)(a), so even if the declarations are filed, it could be necessary to show evidence that there was a genuine intention to reside in Ireland at the time of naturalization, and that the intention changed subsequently. If that intention did not in fact exist, then the minister could assert that the certificate had been obtained by fraud, and if the naturalized citizen is unable to rebut that assertion, the minister could revoke the certificate under 19(1)(a).
In practice, I don't think it is presently very common for countries that generally tolerate (or explicitly permit) multiple nationalities, such as Ireland, the UK, and New Zealand, to seek to denaturalize their naturalized citizens who move abroad.
