Now, that's perhaps a simplistic view, but fairly accurate nontheless.
There seems very little doubt that by the end of last century, Sinn Féin and the IRA had committed themselves to a cessation of hostilities. There is no evidence whatsoever to the contrary. That it took them several years after the Good Friday agreement to begin decommissioning isn't difficult to understand given the history of suspicion and double-crossing that prevailed during the troubles.
You are, I believe (and correct me if I'm wrong) implying that Adams, McGuinness and Sinn Féin were either still engaged in -- or had plans to continue -- an armed conflict by the time Bush was elected (or indeed any time after the July 1997 ceasefire)? Do you have any evidence for that at all? Because as far as I'm aware, there is none.
What I would say, however, is that the Real IRA (the splinter group that did continue the violence post-July 1997) were marginalised and found their financial support disappearing after September 11th 2001. It seems likely that the lack of funds they (the Real IRA) were receiving from the United States had an impact upon their ability to function.
So in that sense, The War Against Terror probably hampered the ability of the Real IRA to destabilise the peace process. But it was a peace process that included Sinn Féin, and had done for almost four years before Bush stole Florida. I'd be interested in any information you have that demonstrates otherwise.
It's also worth pointing out that the Real IRA would have / will eventually disappear on their own -- without the need for an unending global war. Splinter groups are an inevitable consequence of any peace process like Northern Ireland's. But assuming the peace is even vaguely equitable, they eventually disappear as all local support dries up.