automatically updating your game?

Yes, that is possible to do, but you would have to program in support for it in the first place.

If I recall correctly, reserved servers are run independently of regular game servers, and can even run while there are no game servers running, so you could use the http service to let each game server know to teleport everyone to a reserved server, then you could then shutdown all game servers, and update your game, then have the reserved servers send everyone back to a game server.

The reason you should do this instead of kicking is because it could allow people to almost seamlessly continue playing without having to click play again. Also, when doing the kicking option, players could potentially rejoin a server that has yet to be shutdown yet, causing them to go into a kick rejoin loop maybe multiple times.