[Kuruharan]

If the Ring had not been destroyed, there is no question of anything happening but Sauron achieving total victory.

It would take Frodo far too long to truly master the Ring (or as Tolkien himself pointed out, for it to master him) for Frodo to gain anything even vaguely resembling true obedience from the Nazgul, if such a thing were possible. However, he had no time. And in any case, Sauron still retained primary control of their wills, and would have retained them so long as he held the Nine Rings.

Tolkien did indicate the Nazgul would have been rather conflicted, but Sauron was still their master. However, their only purpose was to detain and deliver, as Tolkien said, get Frodo to Barad-dur or wait until Sauron came, whichever happened to be more convenient. Whatever, happened, they would not have flattened Sauron’s army. They would have kept Frodo on the mountain and not taken him anywhere, perhaps gone to the lengths of killing their flying beasts if it proved necessary.