When you create a multi-player lobby, each player/AI has a faction (zealots, imperials, hordes or warlords): different factions are opponents, while the same are allies. Players still have their own units and countries, etc, and act separately on the strategy and RTS maps. In RTS you can send units to help your ally, but there is no direct sharing of resources, AFAIK.
There is no co-op mode where one player exclusively controls the dragon and the other the armies. You can play that way, for the most part, but the person focusing on the dragon still has a base, and can be defeated if it is taken over.
Before everyone switched over to working on D:OS there was mention of a future update for DC at some point. Maybe after the patch for D:OS that adds a couple companions next month(?), Larian will describe their plans for DC.