Keep in mind that early Catholic Emancipation is no guarantee that the Catholics will become/stay loyalists. As Socrates noted above Pitt's argument was that the Catholics would be in no position to dominate a UK wide parliament, but turning that on its head, that could well make independence or at least Repeal more attractive to a newly confident and rising political Catholic elite - in an Ireland ruled from Dublin they could rule the roost.
Labels like "loyalists" and "nationalists" could well have different meanings though. If there is more positivity towards the British state, and if the two sides are not split on a religious basis, there could easily be more of a spectrum of positions rather than two hard camps. A soft nationalist position of home rule within the British Empire would be more likely to come to the fore here.
Of course, the Great Famine will be the determining factor here, so it all depends on what happens with that. Perhaps a domestic Irish parliament means it is addressed more adequately, or if a domestic Irish parliament fails to address it and gets the blame, then the hatred of the British may not radicalise things as it did in our timeline.