no, it's not that it is in test mode, it is that the SMTP Server is not relaying the email message.
double check that you have entered the correct SMTP server address, and that you have entered the correct username and password to access it.
double check the From Email address to make sure that you have entered a valid email address for your domain.
make sure that your test orders do not use the same email address as used for the From address, most SMTP Server will refuse to relay emails where the from and to addresses are the same.
if you continue to have a problem. add the following code to the success page before the </body> tag:
<pre><?php @session_start(); var_dump($_SESSION); ?></pre>
this will output the contents of the session to the page, and will include a email sent success or failure if the email was sent to the SMTP server successfully, you will need to contact the host to look into the SMTP server error logs to determine why the email is not being relayed.