To add to this, this was my online experience:
Recruit Shadowheart with my character
Exchange companion ownership to an online co-op player
Enter the next combat area
When it became Shadowheart's turn, my co-op player lost all the UI elements on screen, unable to control her. He tried passing her back to me using the management window, which worked, and I was able to take her turn, but not able to END the turn. The game could not continue and we had to restart.