Definitely worth an ask, you'll never know more if you don't ask.

Consider that maybe he's seeing you for medication management but the appointments are a bit more like therapy sessions and he does not do therapy sessions? After my pdoc talks to me about the medication, how it's working, then things can be light and chatty for the remaining time.
Yes, because you work together you have another layer to your relationship.

Maybe you'd like to have a session with a therapist, where you can have a 45-50 minute appointment and really get into stuff?