But aside from Cromwell's rule, the truly Puritan societies never really ruled England/Britain.
Plus, as HunttheTroll and Mowque said, the Irish aren't exactly the best ethnic group for labor in the tropics. Pale skin is only one part of it, but the other is resistance to malaria. African populations naturally have some resistance to it, but as European expeditions into tropical jungles and the West Indies have shown for centuries, white people have a tougher time with malaria.
Now, if you wanted to establish some sort of feudal corn-growing estates in North America (and I mean the Pennsylvania-New York area), the Irish would be perfect.