Not if the server admins of both sides are even remotely competent. A good "email server" will at least allow, if not enforce encryption client<->server and (if supported by the other party) server<->recipients_server.
I too scripted a Google Script to run daily, with sending me a reminder or question; & Gmail tags that outgoing mail as a specific label; script pulls that labeled mail every day, archives it, appends the contents to a Google Doc.
