Notifications page cannot be saved without configuring or disabling SMTP
In System > Advanced > Notifications page you can only save changes to any value on the page if the email section is either correctly configured for sending email or the 'Disable SMTP Notifications' box is checked.
In the default case, where neither of those things are true, any other changes on the page appear to save but are not actually put in the config.
No error is shown.
No errors are logged.