I agree with pohnpei in that perhaps national unity is the wrong way to describe it. Unifying in that those who were for or against the war could nevertheless agree on the fact that the loss of 58,000 Americans was a tragedy, and that they should be honored for their sacrifice. Some have argued that it was a healing symbol by allowing both civilians and veterans to connect with those they lost in the war, and to leave offerings, poems, shrines, etc. in a final connection with them (a stunning exhibit of items left at the Wall is on permanent display at the Smithsonian Museum of American History in Washington DC).
The Vietnam War was a very painful chapter in American history and the Wall has allowed many Americans to begin, at least, to process and heal from that grief.