Frankly, I doubt that the Nuclear Bomb was needed Japan in the first place. Firebombings of major cities was killing tens of thousands, a death toll roughly comparable to Atomic Weapons in the first place.
I think it a non-issue that Hirohito would break out of house arrest and urge his people to "endure the unendurable", and Japan would surrender to save the lives of its own people. If not as a result of continuous firebombings, Downfall would be an unparalleled for the Japanese People. While the US army was concerned of fanatic resistance, its important to understand that the Japanese Army Leadership was urging its people to launch a suicidal defense against the United States. They had lost their minds--and more Okinawa like behavior on the Japanese Mainland would force Hirohito's hand.
The problem is that the Nuclear Bomb would probably be developed in the 1960s or 70s without massive government involvement. Indeed, it's possible that a US energy company taps atomic power well before its destructive effects are fully understood.
However, if WW3 breaks out, the A-Bomb will be rushed into development...