This wasn't a therapist relationship, but I once had a friend that I emailed nearly every day. I loved it. There is something very helpful about putting your thoughts into writing and having someone else read it. He answered most days and he shared things back, so it was different than a therapeutic relationship, but it did turn out to be very helpful in helping me deal with my depression. Since he didn't live near me or know any of the same people I do, I could be really open with him. We would still be writing except that he got cancer and died. I think him being able to talk about that with me was helpful for him too.

Since it doesn't seem to bother your therapist and it's helpful to you then why not? If it does bug her she can tell you. It might be possible that she does read all the emails right before one of your sessions though, so I hope you have some other way to get in touch with her if you have an emergency.