I think it's obvious that some of the Sunnis who stayed home probably would have supported whatever the Americans wanted and others would not. Since they stayed home, we can only make assumptions, which is OK because you could make assumptions of similar reliability or non-reliability based on polls. I think though, whether you're basing an assessment on polls or on other assumptions (and I think it's a particularly weak assumption that non-voting Sunnis would have split in the same proportion as voting Sunnis) it's important to note that the conclusion is based on either polling, or election results supplemented heavily by particular assumptions, but it is not based on the will of the people expressed through an election, simply because the nature of the "election" in question is far different from the kind of election we are used to. Their "election" was basically a PR exercise based on armed force and represented nothing more than the managed outcome of a process whose underlying ground rules were dictated by the occupying power. Those who benefit from such an "election" and their American supporters will obviously claim legitimacy but no one other than the direct beneficiaries and their American and other foreign supporters - - particularly no Iraqis - - will ever be able to accept the legitimacy of those "elections."
The bigger problem, however, rests on the assumption that an American-made solution (free and fair elections) would solve an Iraqi problem. The one-size-fits-all assumptions that Americans are prone to make have a built-in rationale that what works for America and similar societies will work for all societies. It's reinforced by an innate belief in American superiority over the rest of the world. It's further reinforced by the simplistic assumption that the only alternative to "democracy" is iron-fisted dictatorship, a la Saddam Hussein, Adolf Hitler, Benito Mussolini, etc. Two alternative models - - consensus models and class-based dictatorships (most famously, the dictatorship of the proletariat) are never discussed, and furthermore, a cartoonish, one-dimensional view of dictatorships such as (for example) the Saddam Hussein regime almost always fail to examine to what extent other interests (class or tribal) are accommodated within the so-called dictatorial system.
IMHO, American-style democracy (one person one vote, winner take all) is simply not workable in a tribalized society such as Iraq and it's a mistake to try to force this down their throats. The British did the same thing to them with a constitutional monarchy, which lasted for about twenty years. They bombed the living shit out of them back in the 1930s, and the leader of the air war against the Iraqi rebels then was Arthur ("Bomber") Harris, later the wartime commander of RAF Bomber Command. Didn't do any good - - in less than 20 years, the government was overthrown in a coup d'etat bringing the Ba'ath Arab Socialist Party, and ultimately, Saddam Hussein, to power. It's hard to accept but this is an ancient society, much older than America, and they settle their own affairs their own way, not somebody else's way.