Yes, but maybe the bombs would have had the same effect, if dropped on actual military targets (or even unhabitated land, but close enough to demonstrate the power) instead of an civilian city.
(a city with military production, sure sure, but they were choosen not because of military value, but because they were relatively undamaged, so the effect of the bombs could be studied. Concern for loss of japan civilian live was never an issue)
Given that the Japanese military wanted to continue the war even after both Hiroshima and Nagasaki, your conjecture is demonstrably untrue. Remember, the military was the primary power in the Japanese government, second only to the emperor, and were the driving force behind starting the war as well. Also remember that the firebombing campaign across all of the other major cities had already inflicted combined casualties far greater than Hiroshima and Nagasaki combined; immense deaths of their own civilians was seen as an unavoidable necessity to defend their homeland.
Remember, it took not one, but two atomic bombs dropped on cities for Japan to surrender. And even after that, there was an attempted coup to continue fighting the war: https://en.m.wikipedia.org/wiki/Ky%C5%ABj%C5%8D_incident
There only existed two bombs at the time. Had the bombs been dropped as a show of force, it is very likely the US and Japan would have to suffer through a costly invasion anyway.
Specifically, the demon core[1]. It was the core-in-waiting for a third bomb if needed, and I believe that the uranium and plutonium production lines were ramping up by that time[2].
40 years ago I wrote a paper on nuclear weapons. My memory isn't perfect and the sources are 40-50 years out of date. But here goes.
The US built a massive manufacturing pipeline to make nuclear weapons. Little boy was a once off. Fat man was basically a functional prototype. And the manufacturing pipeline was running and kept running after the war. How much weapons grade plutonium they had left over after they bombed Nagasaki is kind of a quibble.
Minor elaboration: Nagasaki was not an undamaged city. It had been bombed multiple times by conventional American bombs. But then Nagasaki was just a backup target anyway. Kokura was the primary target for the second bomb but it was obscured by clouds and smoke during the bombing run on August 9 so the plane went to Nagasaki instead. By the time they got there it too was socked in by clouds which is why the Nagasaki bomb fell so far off target.
Why would a demonstration need to be told the japanese in advance?
And a dud could have also happened to the one used on hiroshima.
A shock effect could have been achieved by a bomb detonated close to Tokyo. And with papers dropped, saying, this will happen to all your cities, soon.
(a city with military production, sure sure, but they were choosen not because of military value, but because they were relatively undamaged, so the effect of the bombs could be studied. Concern for loss of japan civilian live was never an issue)