Ultimately this depends on who you ask. The difficulty with these sort of questions is that it's extraordinarily difficult to know precisely what was going on in the heads of the members of the Suzuki government (who ruled from April '45 until the surrender). Even worse, there's evidence that Japanese ministers destroyed official documents near the war's end or just after its conclusion (I can't recall exactly where I read this but it may have been in Taylor & Francis' Aggression, Crime and International Security). This may seriously impede our ability to understand what the Japanese government was actually thinking in the final days of the Pacific War.

Another difficulty with this question is that there's no one "Japan", the decision to surrender must be a joint choice. The country was governed by a Cabinet of Ministers, not a single autocrat, who each had their own ideas and was influenced by any number of factors. Even after both the Soviet intervention and the atomic bombs, there were those within the Japanese Cabinet who opposed surrender.

Further difficulty is added by the fact that the bombs dropped on Hiroshima and Nagasaki (which weren't Hydrogen (H) bombs, they were nuclear bombs) were contemporaneous with the Soviet declaration of war. Japan had been using Moscow as a proxy to send out peace feelers to the Western Allies, but as Soviet-Japanese relations cooled through 1945 this became less possible. It is very difficult to tease apart which factor was more important: the bombs or the Soviets. Everybody agrees that the Soviet declaration of war was a very important reason for Japan's surrender, but historians range from calling it one factor among several important factors, to being the primary cause which made the decisive difference. Certainly there were members of the Japanese government who thought that Soviet intervention would force immediate unconditional surrender, but whether that opinion would have been dominant enough to carry the day is unknown. Naotake Satō, the Japanese ambassador to the USSR, felt that Soviet intervention was inevitable and recommended to his government in mid 1945 that they surrender unconditionally before the Soviets could intervene.

In summary, nobody really knows whether the Japanese were ready to surrender unconditionally. We don't know what would've happened if the bombs had not been dropped. If you believe some historians who emphasise the Soviet declaration of war, then it may have played out almost exactly like it did in reality. Others think Japan may have refused unconditional surrender even into 1946 until the invasion of Kyushu (which itself may not have happened, the Allies may have been content to let the blockade of Japan do its work). In short: there are differing opinions among historians.