So no, offline singleplayer is not working fine by all accounts, it is not intended to work at all, and this was fine with GOG when they reviewed the game. (If you start the game, you will see the message "You need to log in through GOG to access Conquest" displayed in a tooltip over its grayed-out button. It's not something you could actually miss, if you were reviewing the game.)
I'm not seeing anything about this in reviews or elsewhere on Google? The GOG page itself states:
> Please note: The GOG Galaxy Client is required to access online features for Northgard.
But, offline singleplayer seems to work fine by all accounts. I'm actually a bit tempted to buy the game to verify absolutely.