I don't believe that at all. The US when it came it could have done whatever it wanted. Kept the Iraqi Army and police in place and given over the country to a secular Shia Army officer or a secular Shia strongman in exile like Allawi and the average Kurd or Shia would have been happy.
The religious leadership in Najaf can go sit on a nail.
That's good. You think bad guys infiltrating the police and army has been bad these past couple of years? Sorry, that would not have worked. The trust would have been absolutely zero after the first baathist officer assisinated someone.