I'm pretty sure that most of the games on gog released before Galaxy, do not use/require galaxy to play online, nor are there plans to add that functionality (of course some such as the Witcher series, do have achievements).
To answer your question though, yes multiplayer games DO work without the Galaxy client. (though I guess there could be a few that don't, but as far as I know most do. It's probably worth verifying on a game-specific forum, if you have any doubts)
LAN aside, to gain access to online multiplayer, you need to receive a unique serial key from support.
In the case of Unreal Tournament 2004, the download comes with a pre-supplied common key, that all gog users will have. Then to get a unique key, you need to contact support and they will provide one for you.
Also, if you take a gander at the store page for
Neverwinter Nights Diamond, in the about section, you'll find:
"Multiplayer notice: In order to access the multiplayer you must first enter your unique cd-key. For details please follow
this link. "
Hopefully that helps! Regards.