There are too many impossibilities and errors in this to even consider it as remotely factual.

- ICBMs can't reach the moon, or even anything remotely close to it

- Mushroom clouds don't form in a vacuum.

- The fact that some Air Force officer thought it would be a neat idea (if any of this is factual) does not in any way imply that it was even remotely considered by anyone with the authority to make such a decision, any more than seeing a person who works at the Apple store drinking a coke implies that Apple Inc is buying the entire CocaCola corporation.

By "mushroom cloud" they must have meant the ball of dust thrown up by an explosion at/below the lunar surface. That is why Sagan would have suggested it as a possibility for detecting micro-organisms.

But it still wouldn't make a cloud, it would just scatter dust, and each particle of dust would fall back to the moon in a ballistic trajectory (it would not last long at all).

It was probably just a metaphor to vulgarize what he meant. They wanted a big assed bomb.