I think that the answer to the first part of your question is 'yes'. Just imagine two (perfectly rational and highly intelligent) mathematicians debating the truth of an unknown result—say, the Riemann hypothesis. I suppose if you add the caveat 'omniscient', then the need to argue goes away.
It's interesting, I thought about it.. It seems to me that agreement can break when you aren't forced to reveal your model of the world. (For example, you may not even agree to use Bayesian statistics or logic.)
I think it could be useful if we forced the opponent in the debate not just to present argument, but also to reveal their model of the world. That way, they couldn't just poke holes into the argument from an inconsistent position.
