@Tomoyo: Look! You have 666 posts! Take a picture!
I don't think the AI having the map is any great help to it, but I'm not sure. The AI knows the map at the beginning of the game, though it is supposed to pretend it doesn't. In practice, when I've been first to Astronomy or The Great Lighthouse, I've seen the AI wait for me to discover a territory they theoretically couldn't get to, then swarm it as soon as I find it.
So I think they sort of wait for you to discover first, before they acknowledge that they know where something is. So whether you share the map or not, once you've discovered something, they too will know where it is.