Ultramar,
I think that once you have broken the boundary that you and your therapist should have a discussion about it at the next session (hypothetically). I am hoping that your therapist would bring it up, or that you would, so there wouldn't be an elephant in the room.

If your therapist replied to your email, he would be reinforcing your behavior. However, he could also be using flexible boundaries to allow for the fact that you had an overwhelming week. This could easily get out of control, as you say, if it isn't addressed. If I were you, I would ask the question, "What if something big comes up?" At that point, I guess you both would have to define what "something major" means. I think the best conversation would be to get to the root of your need to contact your therapist, whatever that may be. I think how your T responds to this, whether it is to allow two emails a week, or to allow one extra once a month, or not to budge on his boundary should be decided between the two of you, keeping in mind that your T might not be willing to change this boundary for his own reasons.

I am not allowed to email my T, although he did say I could while he is on vacation. I haven't felt the need to email him, but if I started, because email is so easy to write and send, I might be grappling with what I wrote during a really down time. His vacation will be a test for me, and a time for me to learn how to choose what to do when I have x emotions.

But, imagine what it is like for a T to see people all day and to have incoming emails that they don't get paid for, some possibly threatening self harm, etc. I know that I want my job to be over when I get home. That being said, I am not being negative about anyone who emails their T, I think that it is a choice in the relationship.

I think that if the therapist choses to answer your email, that the client has a right to complain because it is therapy, and that is where you can let how you feel out, no matter if you are proud of how you feel or not. This is a perfect chance for the therapist to learn more about the patient as transference may be at play. If both parties are fine with what went on, then that is between those two people and isn't debatable within the confines of that one therapeutical relationship. Every relationship is going to be different. People who have an ambivalent attachment style are going to react differently than people who have a dismissive-avoidant attachment or a fearful-avoidant attachment. People who are ambivalent are going to try to secure a safe base generally, and people who are avoidant, generally, are going to avoid attachment not necessarily as a choice, thus reducing or completely negating a need for contact. So, given that, the therapist might respond differently to the needs of different clients.

Good question