It is only possible if you willing to rewrite and overwrite the core registration/login systems provided by woltlab. Doing so would probably cut you off the official updates as your woltlab suite would be modded and maybe incompatible with certain update(s).
(e.g. do not store users e-mails at all in my database)
You have to make sure your API has a unique identifier for your users if you want to ditch an email address. For example a display name is not always a reliable way to track users as it may be not unique and etc.