Well, first off you'd probably have an ACTUAL rising by the full IRA, rather than IOTL where most of the operation was called off save for a few die-hards in Dublin who refused to listen. Its pretty hard to have a worse execution of the plan than actually occured provided the entire organization is in synch. As a result, the Rising lasts longer and is more broadly based throughout the country, limiting the British government's ability to pull in troops from the rest of the Island to crack down on Dublin as quickly. Given how much of the British military is on the Continent in one spot or another, and that the units left at home are largely 3rd-string and in training, I'd give the movement months before London manages to bring in force that's potenetially overwhelming... by which point armories and cities across Ireland have probably been seized, with Ulster a violent cluster-(French sea lion) as Protestants and Catholics clash over control.
Given that it would be associated with the Reds however, and that the Rising would be alot bloodier and longer than IOTL, expect the cause of Irish Nationalism to get shot through the heart. When the Brits finally DO put it down, it would be touted by the Unionists as a sign that a government from Dublin couldn't be "responsible" that the loyal men of Belfast had every right to be afraid, and the the Empire needs a stronger and more centeralized, not weaker hand. Especially during the sacrifice of war-time, the English would see this as a HUGE betrayal.