Who would have fallen?

[davem]

The man's weakness was that he did not know how to use his weapon yet; and he was by temperament and training averse to violence. Their weakness that the man's weapon was a thing that filled them with fear as an object of terror in their religious cult, by which they had been conditioned to treat one who wielded it with servility.

I suppose the question is whether the Ring would allow itself to be used against the Nazgul - I think this assumes the Ring is morally 'neutral' & has no innate consciousness - which goes against the idea of its calling out to potential users & desiring to get back to Sauron.

Would they have been immune from its power if he claimed it as an instrument of command and domination? Not wholly. I do not think they could have attacked him with violence, nor laid hold upon him or taken him captive...

Again, this assumes that the bearer could use the Ring to make the Nazgul act in a way that they did not wish to - but their desires would have conformed with thehequestion is whether the Ring would have submitted to Frodo in those circumstances.