No. Rich Messages are delivered to the app "Inbox" and can be included in a campaign along with an email or push notification, but are not required. In order to verify if a guest received a Rich Message, you can verify that the corresponding notification from the Rich Message campaign was received or the guest can verify empirically, using the inbox of their app.
If further assistance is required, submit a ticket to Punchh Support. (For help submitting a ticket, click here)