It's not about the therapist, it's about your therapy. It's a therapy boundary (not the therapist's boundary) and your T is going to try to do whatever s/he deems is most helpful to you in the moment. You can send a zillion emails every week if you want to, you would be breaking the agreement you and your T decided was best for your therapy at that time. Your T perhaps with the agreement agreed they'd answer one so the others would probably go directly to T's trash/spam for all one knows. But I bet the discussion would be about you breaking your half of the agreement, not about T and what s/he is doing.