PUT and POST are designed to be used to create and update resources. The server may or may not have a database behind it. It might use a local filesystem, or it might handle anything in memory. It's none of the client's business. It is certainly common to have business logic on most servers which provide APIs.
Use PUT/POST to send up the email address to the server. The server checks to see if the email address is (a) valid, and (b) allowed. If it fails either check, return a relevant response to the client as documented in the RFC. I would go with 403 Forbidden, which indicates a problem with the data being sent up to the server. Use the entity in the response to detail what the problem was with the request.