I don't believe it could have occured, not without massive loss of life/ethnic cleansing at least not in the modern period.
Historically the best chances of a United Independent Ireland were 1) What if the freak blizzard of 1796 had not occured and Napoleon's forces had arrived on the Cork Coast in December of that year instead of turning back? The Irish Militia and the British Garrison was so weak the country would have been outrun quite quickly (and massive revolts would have taken place across the country... massive loss of life here too) perhaps even before Westminster could put an army together. Some sort of French quasi-puppet regime would have been installed with someone like Henry Joe McCracken as the Napoleonic stand-in (Who wants to be King of Ireland?). But if this occured European and World history would have been very different and there are doubts about the viability of this state so...
2) No Norman Invasion in 1169 in the first place and the Gaelic Chieftains finally conquer one and other enough that someone becomes powerful enough to rule over the whole Island without local chief immediateries... this was on the way to happening before the Normans intervened, the major Gaelic Kings were growing more powerful and powerful over the minor ones so perhaps give it a century or two...
Great....
Ireland was never 'unified' in the first place so I don't rate the chances of an independent all-Ireland state coming into being very strongly...
Ireland was very unified before the War.
