No, continuing the war will not irreparably damage the U.S. Military, because the U.S. Military is extremely strong. The U.S. Military is powerful enough to withstand being stretched thin, and that includes continuing in Iraq, if necessary. That is not to say that continuing the war there is a good use of resources, but the United States military is strong enough to continue there without irreparable harm.
I don't think continuing the war would have irreparably damaged the US military, but I definitely felt that it was well past time to withdraw the troops. The United States has one of the biggest Army's in the world and spends much more than any other country on military. Our military will not come out damaged.