This happened in the midst of WW1 and I know thousands of Irishmen served in the British armed forces at the time. Is there any record as to how some reacted to this?
German interrogations of prisoners of war seem to indicate that it had little affect on the morale/dispositions of the Irish troops. Press censorship meant that it was difficult for Irish troops at the front (primarily in 16th (Irish) division) to get much news about the Rising. All they would have been aware of was that it failed, and a number of Irish-Australian prisoners interviewed brushed it off as insignificant, in light of failed rebellions in Ireland's past. Roger Casement, who helped to organize support in Germany for the rebels attempted to raise an 'Irish Brigade' from POWs, and this failed miserably. The fact that 16th (Irish) Division went on to achieve great success at Ginchy on the Somme battlefield in early September further indicates that Irish morale was at least good, regardless of events in Dublin.
The actual rising was an unpopular action that failed to inspire the uprising they had hoped to motivate (initially at least). It was the later treatment of the rebels that changed the mood and turned the Easter rising into the turning point that it was.
Indeed as you would expect, it was Irish British Army units that initially responded to put down the rising. The 15th Ulster and 25th Irish reserves were instrumental in reacting as were the garrison units (royal Irish rifles, royal Dublin fusiliers, PoW Leinster regiment)
You also have the very brave actions of the trinity college OTC students in defending the college.
So during the rising, you could quite easily state that the reaction by the Irish in the British army ranged from having little effect on the front as /u/DuxBelisarius covers, to actively repressing it in the case of the regiments in Ireland.
Easter Rising 1916 Birth of The Irish Republic by Michael McNally
Alistair Kerr - current articles on the OTC for the anniversary celebrations this year.