People can come and join as they feel like it, sort of. The game will not run until all player slots are full. The host can add or disable player slots, via the manage players button on the menu. However, it is somewhat awkward and slow, plus, if someone new comes in, they must either start with very little (they are given a home core, a "mini-home", and a little bit of resources, and that's it), or hop into someone else's slot, which the new player will have to deal with how the old player did things.
To be honest, I'm not really sure how AI war chooses which option when a new player joins. I do know that if you have already participated in that game, the engine will try to put you back into the same player slot, so you don't have to worry about players joining back in the right order when loading from a save.