What would they do?

[Inziladun]

Originally Posted by Belegorn

I don't think this has much to do with Frodo discarding the Ring, but he has offered to give it up to others and when Tom asked to see it "Frodo, to his own astonishment, drew out the chain from his pocket, and unfastening the Ring handed it at once to Tom."

Yes, I think that incident was more to do with Tom's status as "Master" at that particular place. Whatever the secret of Bombadil's power, Frodo's (and the Ring's) will was not strong enough to have any chance of defying him.