I really, really want to buy this on GoG instead of steam, and HUGE kudos to HelloGames for actually bringing MP, I'm impressed.

Does the current beta have any sort of LAN functionality at all? Server files for private hosting? Any intention of adding such functionality in the future, if not?

I'd be appreciative if anyone playing the beta would mind uploading screenshots of any multiplayer settings/connection screens, such as they are (and maybe take a poke around in the .ini files).

I would assume you will only be able to access the multiplayer function through the GOG Galaxy platform.If your goal is to not have to log onto the internet to play or a gaming platform to access multiplayer I think you are out of luck.

If No Man's Sky had any sort of LAN capability we would have gotten at least that functionality when NEXT released.

If your concern is keeping griefers out of your game there are setting that only allow player who have your permission into your game. And remember the GOG player base is much smaller than Steam. And since most of us purchased NMS when it was not a multiplayer game and chose GOG to play offline, I would say it is safe to say the actual number of GOG players using multiplayer will be pretty small. Most of the players who really wanted multiplayer have already made the jump to Steam.