You're being highly speculative. It's impossible to say what Tolkien would have envisioned in that respect.

Gandalf claims not to know a great deal about the Rings of Power. He and Elrond did form their own opinions, but there was at least one session of the White Council where (it appears) the Rings were discussed openly and information was shared (at least, Saruman lectured on what should have happened to the One Ring).

There are a lot of "IFs" even in my qualified response. It's impossible to say who is right or wrong. If there is a definitive answer in anything Tolkien wrote, I cannot think of what it might be.
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