Assuming we get multiplayer working -- which seems likely at this point -- then the idea, in those circumstances, is that world = server. So you'd set up a server for you and your friends, and whoever wanted to would run it. Then anyone who wanted to connect could do so, with or without other players, and you play while you're there and then exit. The server itself persists beyond any of the players, and unlike AI War there's no reason to hotsync, etc. It's basically exactly like Minecraft, or any FPS game for that matter.
The worlds generated by a multiplayer server would be entirely compatible with single player and vice-versa. So you could play solo if you want without the server, then turn on the server for some co-op. Though, you can also play via the server for solo if you want, it doesn't limit the players to 2+ for that (though why you'd want to if you never have more than one person would be a question -- but I digress).
The servers should ideally be able to handle 16 players, but that remains to be seen. Certainly at least 8, but possibly more than 16. It might depend on your network connection where the server is hosted as to how many you can really support, actually.
If you play multiplayer with a lot of different people who don't want anything to do with one another, you will indeed need to have multiple worlds. If you have a group of friends where there's only ever 16ish of you online at one time, and someone doesn't mind using their bandwidth to have the server going all the time, then you could all just share one server and that's that; no need to ever have more than that one world for any of you.
All of that is speculative -- but those are the goals, and they should be reasonable based on our technical design for this and our past experience with AI War, etc.