You can host a dedicated server and basically the whole game is then running in your LAN only, no further internet connection required.
BUT as mentioned above, every time a client connects to your dedicated server, it needs to authenticate it's steam key. I'm not even sure if the client sends the request or the server tries to verify it. So yes, practically you will need an internet connection for being able to connect. But a slow internet connection is enough for that as the game itself doesn't need it. Even a mobilephone hotspot would do that and it will not cause massive amounts of data transferred.
Anayway, it would be far nicer, if the steam offline-mode would do it without any internet connection at all.