I saw my T yesterday. I am a new patient of hers, so I don't know her patterns yet, but she did mention that she had read my first email to her (which she did not respond to) and now she had to reread it again a bit to remember what it had said. (It was about my goals for therapy). When she did peek in at it, she recalled it and then we spent the whole session going over my goals for therapy and what I wanted more deeply and thoroughly than what I had stated in the email. She asked me what I meant by a few of my goals, so I had a chance to really elaborate and give her examples and ideas. I also thought of a few things I had not mentioned in the email.
So, looking back on it, it is OK by me that she did not reply to the email. However, I do not know if that will be her way of dealing with my between session emails every time or not. We shall see. I did not think to ask. (Also, since there was nothing urgent in my email, there may have seemed to have been no reason to reply to it).