I realized that Mod messages/suspension notices are not delivered to the inbox.
I'm not sure why that's so. With most activity being delivered to the Inbox, something as important as Mod messages should also be delivered.
You may argue that the suspension notice is sent to email - but if there's no email address provided, once a Mod Message has been issued, if there is an overlay(I've never been suspended, so don't know), dismissing the overlay would mean that there's no way to read the mod message.