Indeed, Musashi would have to have been an Avatar, were he transported to The Last Airbender's universe.
My first major question about this very interesting conceptualization of Avatar would then be: is being an Avatar just a one-in-a-million trait (assuming the population of that world is a million)? Because it seems like a rationalist Avatar would prefer not to be the only one on the planet.
That's a good point. In this version, the Avatar doesn't have to be a spiritual Chosen One - he/she could just be genetically lucky the way extremely high-IQ people are in our world.
Edit: However, I think that would defeat the point of fantasy rationalism, and might make the world too mundane. It would, however, be really interesting to see Aang go to the Spirit World and try to convince whatever spirits originally created the Avatar to make another one, possibly one with more raw intelligence to be more effective. (And then maybe deal with the fallout if ...
I've been enjoying reading Less Wrong fanfiction, and I wanted to suggest another fandom that should have at least one rationalist fanfiction: Mage: The Awakening. It's a roleplaying game about "modern sorcery." My description can't really do it justice...