I think we tend to agree. However, I would point out that whilst culture was not adopted outright (particularly thinking of religion here, where the settler culture 'failed' for lack of a better word,) in terms of linguistics the settler culture very much won out in Ireland. Then there is the fact that a large percentage of the population have English or "British" ancestry (a close friend of mine from Ireland remembers her family hiding IRA members during the troubles, but simultaneously being told by her parents not to mention she had an English grandfather.) I think it would be relatively hard to give percentages on which percentage of the Irish population today are directly descended from the settler population, but I think estimates are generally fairly high (if not the majority, but I am not well read/don't remember enough of the exact figures on the subject.)I think we are on more or less the same page, but disagree about definitions. I would say that you need the settlers to be the dominant element in the population, and the culture of the dominated element to be minoritised completely. That didn't quite happen in Ireland, there were settlers but they never outnumbered the natives or succeeded in forcing them to adopt their culture. They came very close in Antrim and Down, where religious conversion of the natives was very high, and around Fermanagh where there were points when deadness of the natives was very high. But the Irish Protestant and Catholic cultures hybridised, so you had weird effects like native Irish-speaking prods and the mass retention of a Catholicism that was the main instrument of oppression of Irish popular culture and one of the drivers of anglicisation.
Today Ireland's identity is principally nativist and its population principally Catholic, so I don't think we can call it a successful settler colony.
The POD was before 1900 and the settler population were definitely the dominant group in 1900... I suppose the OP never stated how long the settler colony has to last, which brings us back to definition. With a modern Ireland that is decidedly part of the Anglosphere with good relations with the English speaking world etc, I would say that it is a pretty successful settler colony (and if not the Republic, than certainly the North.) Certainly more successful than the Baltic German example given above.
I suppose the OP needs to clarify his definition.