What I mean by embedding the image is that you are including the binary data in the HTML for the email.  What you show in your question above is not embedding the binary data but rather embedding an image link, which will still render as an image when the email is opened.  But the actual contents of the image are not contained in the email.  Instead, the email client must reach out to the server to load that image that resides on the server.  When you are testing with the server name, are you including a fully qualified computer name (i.e. with domain) or just the NetBIOS computer name?  If using a NetBIOS name, that should be interpreted  by the browser as a Local Intranet zone web site and will attempt to pass through the user's domain login credentials when met with an authentication prompt.  If using a fully qualified name, this will normally be interpreted by the browser (or email client in this case) as being in the Internet zone and will not pass through Windows authentication.  You can generally solve that by adding the FQDN of the server into the Local Intranet or Trusted Sites zone (either manually or through AD Group Policy).  If you're really trying to embed the binary data for the image into the email message so the client doesn't need to connect to the server at all, then the easiest way to do that is to load the image in Paint or your browser, right-click copy the image, then paste into the Notification editor in Design view.  After doing that, if you switch to the HTML tab in the Notification editor, you should see the image data as Base64-encoded text.