I can say from personal experience that
1. nobody who owns the GOG version is paying much attention to the MP or the GOG forums as I've been unable to find more than one person to play with, and
2. starting and playing MP games works fine in my experience. Restoring a saved session, on the other hand, has never worked for me, and support has not replied to my support post since July or so. Make of that what you will, to me it says Stardock is not all that interested in Galciv3 multiplayer.