The short answer is no. The entire war began on a false premise: that Iraq was hiding weapons of mass destruction. Because those weapons did not exist, the American forces were left with murky and unclear objectives, while facing strong ideological resistance. After the hysteria surrounding 9/11 and the War on Terror finally subsided, it was hard to imagine how a clean victory could have ever been achieved.
The American invasion of Iraq shortly after 9/11 was not justified or legitimate. There was no feasible evidence that the Iraqi people were manufacturing or harboring 'Weapons of Mass Destruction" and many lives were lost simply because the U.S government was fishing in the dark. I do not believe it was legitimate in the slightest.