Bill Essary provided the following as a work around for using a Team Foundation Server email notifications with an SMTP server that requires a user name and password.

TFS does not directly support using a username and password to connect to an SMTP server but it is possible to work around this limitation by using an SMTP virtual server on the TFS AT.  That virtual SMTP server can be configured to provide the authentication credentials that the “real” SMTP server needs when relaying messages.  Please consult the following links for more details:

As mentioned in the MSDN forum thread, Pete Sheill provides information on tracing the TFS interactions with the SMTP server in How to verify Tfs is sending emails.