It was the first physical shot of the war in the proximity of the war and directly related to the event that initiated the war, so yes. It initiated the hostilities of physical warfare.
On that basis one could just as easily claim that the hostilities were actually intitiated several months prior when the south fired on the Star of the West.
One could probably find any number of isolated firings, skirmishes, and other pre-war events by either side. But none has the proximity to the war that the Harriet Lane did. For all practical purposes it was the first shot of the war.