I'm pretty sure Mystic totally locks us out of theurgy, it's path of the gods are inscrutable. Theologian is the path of integrating them more totally into her arcane world view.
"Theurgy" has never actually been defined and different people in-thread use it to mean different things. Without defining Theurgy any statement about it's plausibility is meaningless. (Hence why BoneyM never talks about theurgy, because it isn't even a distinct thing.)So we know that Mathilde can't use divine magic ever, but Theurgy is firmly in the camp of "try it and find out."