I dont think so actually, as far as I know it works like a complete mind control from that point on. They only appeared weaker in the past because Kabuto was manipulating multiple bodys at the very same time. I would even say that edo with own will is weaker, because he can give out information about his jutsu to the enemy and even work against the users will directly (Hanzo for example who stabed himself).
But once the user has taken full control of the body, he can make every move with it that he wants to do, and if the body gets tricked in this state, then only because the user himself got tricked at the same time.
At least that is how I understand it.