Whatsapp disagrees, from the article:

...a WhatsApp spokesperson confirmed the researchers' findings, but emphasized that no one can secretly add a new member to a group—a notification does go through that a new, unknown member has joined the group.

Well, it has to send the public key for the new group member to the client, so the client will encrypt messages for them with that key. So the server HAS to notify the client of a new member if they want to intercept any messages.

No, the notification of a new member joining is always sent. Subsequent messages might be blocked.