Go here:
http://lcweb2.loc.gov/frd/cs/iqtoc.html#iq0020This is the Library of Congress country study, circa 1988. A couple things to remember. (1) This was in the 80s, when Iraq was our friend. (2) In the interim, there was the DaddyBush "I've got your back, oops! I don't got your back" Shia uprising post DaddyBushWar.
Nonetheless, this very interesting little book does not appear to be terribly propagandistic, and may be one of the more level-headed treatments of Iraq available on the web.
From the section entitled "Sunni-Shia Relationships in Iraq":
Until the 1980s, the dominant view of contemporary political analysts held that Iraq was badly split along sectarian lines. The claim was that the Sunnis--although a minority--ran Iraq and subjected the majority Shias to systematic discrimination. According to the prevailing belief, the Shias would drive the Sunnis from power, if once afforded an opportunity to do so.
Nonetheless, the theory of sectarian strife was undercut by the behavior of Iraq's Shia community during Iran's 1982 invasion and the fighting thereafter. Although about three-quarters of the lower ranks of the army were Shias, as of early 1988, no general insurrection of Iraq; Shias had occurred.
Even in periods of major setback for the Iraqi army--such as the Al Faw debacle in 1986--the Shias have continued staunchly to defend their nation and the Baath regime. They have done so despite intense propaganda barrages mounted by the Iranians, calling on them to join the Islamic revolution.
End quote.
In other words, it may be that nationalism trumps sectarianism. It certainly does now. For the endless what-if-the-tables-were-turned exercise: If the mighty Muslim invasion force had taken the USofA, there's little doubt that the Dem/Repub and Fundie/Infidel forces would unite to toss them out. Once that was done, I doubt the various factions would set upon one another; more likely we'd return to our current state of nattering chaos.
What's more, it's entirely possible that the majority of Shiites recognize the fact that not all Sunnis were Baathists, and not all Baathists were members of the true ruling class. Just as we recognize that not all Republicans are blood-dripping neocons.