I would have been scarcely surprised to find Iraqis willing to fire on fellow Iraqis at the Americans' behest. After all, their targets today could well be their rulers tomorrow, even if there is no brotherly feeling.

A recent historical parallel may be the last years of the British Aden Protectorate. Before leaving, the British tried to create a Federation of Sheikhdoms, with its own defence force, the Federal Regular Army (or FRA). When radical independence movements developed, it was instantly clear that the FRA could not be used offensively against them. It did not actively mutiny (although a Police unit in Crater did), but that is as far as its loyalty to the nominal Federation went.

After the British left in 1968, the FRA proved to have been extensively penetrated and influenced by one of the independence movements, the NLF; and it had absolutely no qualms about firing on other independence factions in the brief scuffle for power which followed.

Working from this, I don't think any military unit or political body established by the US in Iraq (not counting Kurdistan) can be relied upon in the long run. Knowing that they will have to live with those Iraqis who have resisted the US and can therefore claim nationalist legitimacy, they can be expected to be laying off their bets from the moment they are established.