The problem was that Japan initially only offered to accept a conditional surrender which not only included the maintenance of the emperor, but also protection of it's officials from prosecution for war crimes, and recognition of it's right to occupy an empire outside of the Japanese islands. A lot of people criticize the atomic bomb by saying the Japanese offered the same conditional surrender the United States accepted later anyway, of the emperor staying on the throne, which is not exactly true. Not to say I think the atomic bombs were necessarily necessary. The peace faction was already gaining ground, and Hirohito was coming to realize his great victory was never going to be. And the pressing matter was the entry of the Soviet Union into the Asian/Pacific War. The atomic bombs are argued as the only mcguffin which stopped the Japanese, which is not so and is Amerocentric. I would argue the atomic bomb gets thrown in with those other factors as a tacked on article in the argument. There is a definite disconnect between the argument that the Japanese were so gung ho that they would never ever surrender, and the argument that the might of the atomic bomb forced them to surrender, and relation between those two thoughts in that the Japanese were never going to surrender so the atomic bomb was necessary to make them surrender.
Did the atomic bomb play a role in the Japanese surrender? Likely. However, I would argue that the other factors were pressuring for surrender regardless. In such a scenario, the U.S. invasion would not have been necessary. However, we do enter into the moral debate of those days, weeks or months more of suffering before the war ends in surrender, and the moral issues therein. And without the atomic bombings, Japan would lack the excuse it has for not reflecting on it's sins in the war. The atomic bombings were a tragedy, which no one can argue. However, Japan willfully committed atrocities, and it is disheartening that there does exist such a strong thread in Japanese society of burying it or acting like Japan was not an aggressor, or that it was only as bad as it's enemies. Germany cannot and does not do that, and it regularly commits penance for the sins of Nazism.