Can you please check what is the status of the e-mails that are sent? Here is how the Newsletters module works:
1. When you send the mail, the module connects to a web service (WebMailingService).
2. The Service connects to the SMTP server
3. If the SMTP accepts the connection and the letter, Web Service reports back to the module that the letter is sent, and it should appear in the Sent directory (just like in Outlook). Otherwise, the mail is reported as Failed one.
Once the mail go beyond the SMTP, we do not keep track of it. Perhaps you should wait for a while, Googe service might report something.
All the best,
the Telerik team