"I am an Irish speaker."
Translation:Is gaeilgeoir mé.
That pronoun in Is é Pol uchtaran na hEireann is a "subpredicate" whose role is to separate the copula from the definite noun Pól.
As gaeilgeoir is not a definite noun, it doesn't need to be separated from the copula, and the standard word for a classifactorial copula remains - Is Gaeilgeoir mé.
There is a difference between classification sentences ("X is a Y") and identification sentences ("X is the Y"). And personal names like Pól can cause exceptions to those patterns anyway.
Is Gaeilgeoir é Pól - "Paul is an Irish speaker".
Is é Pól an Gaeilgeoir sa chlann - "Paul is the Irish speaker in the family"
Is mise an tUachtarán - "I am the President"
Is uachtarán mé - "I am a president"