Depends on the actions of Germany and France, primarily. I'd weight towards 'no': with Home Rule in effect, Ireland will be, how to put it, a bit more unrestive, and that would distract Britain a bit, and make a few more politicians less inclined to go to war with Germany right now. Given that the British government was disunited about going to war in OTL, when they had been handed a clear casus belli, and Ireland was not that unrestitive, I'd say that Britain could well stand aside for at least the first year, if Germany doesn't do something even more stupid then they did in OTL.
That is, assuming the situation in Europe isn't used to push the enforcement of Home Rule forward, as it was in OTL: but, given that Britain isn't in war yet, in that situation, that would be more unacceptable, and could in itself cause more unrest then OTL.
Now, one could remember that not entering that year, and not entering at all, are two different things: but, on the other hand, I'd also say that when just how bloody a modern war is, support for entering the war could drop a bit. Really, it depends on the actions of Germany and France: does France do something stupid? Does Germany hand Britain another clear casus belli soon afterwards? The course of the war itself could affect the answer, so I can't answer the poll.