In my personal opinion, the answer to this is an emphatic no. While it can be argued that dropping the bomb ended the war more quickly thus preventing the loss of American lives, that cannot be prov en. There is a great deal of evidence to suggest that Japan was ready to end the war before the bomb was dropped.
Among thos Americans who felt that dropping the bomb was, essentially, overkill was Dwight D. Eisenhower. Eisenhower initially supported the idea, but then revised his opinion stating:
I was one of those who felt that there were a number of cogent reasons to question the wisdom of such an act. ...the Secretary, upon giving me the news of the successful bomb test in New Mexico, and of the plan for using it, asked for my reaction, apparently expecting a vigorous assent. "During his recitation of the relevant facts, I had been conscious of a feeling of depression and so I voiced to him my grave misgivings, first on the basis of my belief that Japan was already defeated and that dropping the bomb was completely unnecessary, and secondly because I thought that our country should avoid shocking world opinion by the use of a weapon whose employment was, I thought, no longer mandatory as a measure to save American lives. It was my belief that Japan was, at that very moment, seeking some way to surrender with a minimum loss of 'face'. The Secretary was deeply perturbed by my attitude...
Herbert Hoover, too, was revolted by the use of a weapon that killed so many innocent people in a war that was ready to be ended through diplomacy:
I am convinced that if you, as President, will make a shortwave broadcast to the people of Japan - tell them they can have their Emperor if they surrender, that it will not mean unconditional surrender except for the militarists - you'll get a peace in Japan - you'll have both wars over
There are many other well-respected Americans, military and political figures who were well versed in the situation, who echoed these sentiments. Military attacks that are directed at civilian targets should be a last resort, if and only if all efforts at diplomacy have failed and show o signs of doing anything more than continuing to fail in the future. This was clearly not the case in this situation. Could the war have ended diplomatically and without the bomb - it is my belief that it could have, but we will never know because the choice was made and the rest is history.