“Is it necessary” would of course be ‘no’. St John Vianney wasn’t considered an intelligent guy by his contemporaries but he is the patron saint of priests and one of the or the most recognized Confessors in history.
A modern theology major (Catholic) is a hybrid of philosophy, spiritual reading (particularly in the study of revealed texts), and possibly some communication/leadership related courses.
“Intelligence” is a nebulous concept and when we refer to intelligence in the singular, we’re really referring to a complex and poorly understood vast combination of cognitive processes.
The idea of emotional intelligence is even less understood and some would argue that it isn’t ‘a thing’ at all, but taking emotions into account for a minute, one must realize that emotions can often either enhance or get in the way of the intellect. For example, a person might have an extremely high intelligence (whatever that is), but if they are constantly getting entangled in confirmation bias, a hypersensitive self-esteem, discouragement, etc., then the chances of having a prestigious career or even an exceptional life at all are remarkably low since encountering resistance from other people and from within is guaranteed. How well that emotional makeup mixes and cooperates with the intellectual faculties of the person is going to reflect their overall professional character.
Peace.