If I create a List and then Manage the Permissions to Add "Everyone" or "Everyone except for external users", and "Send an Email Invitation" is checked, then where does the email go? Will it actually send one to everyone in the organization?
Actually, SharePoint does not email the Everyone or the Everyone except external users. This is by design and has nothing to do with the user info list. More information can be found here: https://support.microsoft.com/en-us/kb/2987820
But in a nutshell, when you use the everyone group or the everyone except external users you will just be assigning security, SharePoint does not provide an email when these are used.
If you check the user info list you will see there is no email address associated with "Everyone except external user"