What notifications are sent out when using Modules in Canvas?

When Modules are created and published, notifications are not sent out. 

The only time notifications are sent out for content items within modules is when the content item itself is published, regardless of whether or not the module itself is published or not.

Note: If you publish the entire module instead of the individual item within a module, then all of the items will be automatically published within the module. The only exception is if you have already manually published one of the items within the module, then the auto-publish feature will not automatically publish all of the other unpublished content items within the module.

As noted in the official Canvas Notifications PDF, Modules are not included in the items that trigger notifications.