I use email a lot in my therapy- I have no idea if my therapist has a policy around it generally. I just started writing and have always been super-specific about not needing a reply, which for me is essential- I don’t want him to feel obligated to respond, and I don’t want to make myself anxious waiting for a reply. But writing helps me work through a lot of stuff on my own in between sessions.

Perhaps you could trust your judgement on whether it’s a good idea for you? And then discuss it when you see each other next. I would imagine therapists have a wide range of opinions on how their clients might use email, so it’s a little hard to predict what a therapist might say on the topic.