My therapist encourages email contact, she almost always responds, and we have had some profound exchanges (we work much better via email than we do in person, probably due to our mutual hostility). She has never told me that I email too often and nor has she even hinted at the idea that I should stop contact outside of session. However, I am convinced that every email I send will be the message which pushes her over the edge and she will tell me to stop and probably even terminate therapy altogether. My point is, it probably wouldn't matter how much reassurance they gave you about emailing, you would feel anxious about it.