"I would say of course they had a choice. We all do."
Yeah, I think you've summed up the whole point of the thing in two quick sentences.
"I believe even then, (influenced by the Ring) Frodo intended to claim the Ring and attempt (vainly and foolishly) to challenge the Eye."
I don't think so, probably he was thinking it, but still intended too destroy it, though at the end he could not, as none of them could have.