That's the question currently being asked by senior American commanders in Iraq. And the answer, according to StrategyPage.com is "not yet:"

Al Qaeda in Iraq has lost thousands of members over the past year. The group is fragmented and has lost the support of the local populace and Al Qaeda senior leadership.

AQI is unable to gather large forces any more, mainly because Iraqi and American military forces and Concerned Local Citizens confront and defeat it. Already, the group relies on regional commands and soon those commands will fragment. This has already occurred in Anbar Province. Areas of AQI activity remain isolated in the country. Being isolated, AQI becomes easier to target. Militarily, AQI is staring directly at defeat. The 2006 US Army Counterinsurgency Manual states, “Victory is achieved when the populace consents to the government’s legitimacy and stops actively and passively supporting the insurgency.” In the past month, the Concern Local Citizens program has exploded. Starting with the Anbar Awakening, it is now over 67,000 strong consisting of Sunnis, Shiites, and Former Regime members.

The debate over whether to declare victory, however, continues. First, it adds to the rhetoric of progress in Iraq. From this rhetoric, the media-sensitive Al Qaeda will suffer further reduced morale. At home, the debate will help direct the focus on developments within the country.

The caveat remains; AQI is still a viable terrorist organization.