Yes, the made generals got adopted. As to would a captain leading the army have been adopted I don't know. It is most certainly possible as since I had 4 family members and 12 provinces, the game does start giving more adoptions/moth. All I can say is that all of the made generals I had were immediatly either adopted or moth upon their first combat. And it was them as the name on the papers was the same as made generals name. In addition no new unit appeared as it does when you get a moth for a captain.