Not even close. Fat Man and Little Boy, as post-war access to Imperial Japanese records show, were instrumental in convincing the Emperor to surrender. The Soviet invasion was ultimately not largely consequential to the surrender.
For a more public example, look at the Emperor's surrender speech:
Moreover, the enemy has begun to employ a new and most cruel bomb, the power of which to do damage is, indeed, incalculable, taking the toll of many innocent lives. Should We continue to fight, not only would it result in an ultimate collapse and obliteration of the Japanese nation, but also it would lead to the total extinction of human civilization. Such being the case, how are We to save the millions of Our subjects, or to atone Ourselves before the hallowed spirits of Our Imperial Ancestors? This is the reason why We have ordered the acceptance of the provisions of the Joint Declaration of the Powers.
If you want cruel and unnecessary, the firebombings are much more condemnable and less justifiable than the atomic bombs. And killed more civilians.