AlQeda is anything but Shiia leaning. Indeed, AlQeda would classify Shiites as heretics. Anbar which is dominated by Sunni Arabs has a strong core of nationalist Iraqis and were big Baath party supporters. They reacted quite violently to the US intervention in Iraq because it meant a loss of political power and status...the Shiite majority emerged as the new power in Iraq (arguably, as the majority, that is how it should be).
In any event, as I understand it, the transformation in Anbar -- which, in fact pre-dates the "surge" -- has occurred because AlQeda (which is a small but volatile and deadly force) is mostly made up of foreigners -- i.e. Arabs (SUNI ARABS) from other Arab countries...notably Saudi Arabia as well as other "foreigners." The Sunni Arab nationalists of Anbar reject this outside interference as antithetical to their more nationalistic (as opposed to pan-Islamic) vision of Iraq, and have increasingly sided or sought the help of the US because -- the enemy of my enemy is my friend (a very old and well employed strategy among Arabs...not to mention non-Arabs, recalling our own alliance with Stalin during WWII).
Anbar, however and as has been pointed out by many independent commentators, is hardly a model for how to sustain whatever the surge was supposed to accomplish. The violence there was mostly Sunni on Sunni. It involved foreigners -- non-Iraqis. Some claim that those we are helping to calm Anbar could just as easily turn against the US as the policy shifts in Iraq. The real tension in Iraq is that between the Sunni minority (the beneficiaries of Baathism and Sadaam) versus the long oppressed Shiia majority who shares a religious belief (though the are Arabs not Persians) with Shia Iran.
And, of course, the above equation leave out Kurds who have carved out a relatively successful quasi-state in the North, but who also have a bloody history with the Sunni and who have a problem with the Turks.
In short, the model here may not (and likely won't) be replicable in areas where Shia nationalists might fight with religious Shiite militia supported by the Iranian, or disputed zones where Sunni and Shiite are vying for leverage and control. Note that large sections of Baghdad, for example, have essentially been ethnically cleansed...Shiia taking over Sunni neighborhoods, and vice versa....such whole scale population transfers are always good for building lasting peace...just ask Pakistanis and Indians.
In any event, do not confuse the Shiia with AlQeda...even if, under some circumstances, there may be a temporary conflation of interest (for example, there is some indication that the Shiia in Iran are now helping the Taliban).
IMO, one of the great strategic blunders this Administration has made -- in real-politic terms, not tactical or implementation -- is that given what its stated policy was (attacking Iraq because it was developing WMDs and the hint that they were involved in 9/11), we should have first have found a way to make peace with Iran. They loath and fear AlQeda, and are hated by AlQeda. They have huge influence over the Iraqi Shiia (which they are now exercising) -- who are the majority population in Iraq. But than, of course, thawing relations with Iran would have been a real bother to our Sunni Arab allies in Saudi Arabia. In any event, if we are talking Democracy in Iraq as a definition of success...than we are talking a Shiia dominated Iraq pure and simple...or we're talking a split Iraq... or a return to a murderous Saddam-like Sunni strongman to come out of a place like Anbar who we help put down the majority population.
See the mess we've stepped in?
