Yes. If the Iraq War had never happened, Iran would no doubt have been inciting Shia activity against him. Combine that with the atrocious economic state Iraq would likely still be in and the better organizing potential (Saddam was removed from power before Facebook and Twitter had come into existence), and he would probably have met the same fate he did IRL - hanging from a gallows after being pronounced guilty by a kangaroo court. It just would have happened six years later and at no cost in blood or treasure to the United States.
More likely the Iraqi Civil War would right now be the big news story, overshadowing the similar conflict in neighboring Syria.
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