Why: Currently I am using Mimemail to send HTML-formatted messages; however, because of the configuration of my server, these e-mails are often being recognized as spam. To reduce the chance that they will be recognized as spam, I want to use the SMTP Authentication Support module.
Yes. We can use the Mimemail + SMTP Authentication Support. Plz check the link http://drupal.org/node/1200142 and check the part : Alternative Approach: Mail System + SMTP + Mime Mail
http://drupal.org/node/1200142 is a good way to set up Drupal + Mimemail + SMTP. It needs also Mail system module (as a dependency of Mimemail).
There is a trick: When using the Mime mail__SMTP bridge for both Site-wide default MailSystemInterface class and Mime Mail module class is OK when sending email without inline images (I didn't try with attachments).
But when trying to make Mailmime embed images, it results in a PHP Mailer (Drupal) error saying "Mail body empty".
To make the system work,you have to set Site-wide default MailSystemInterface class to MimeMailSystem.
I'm not sure this is a reliable way because it could mean you are not using SMTP connection at all. Though, when you run a SMTP test from SMTP module configuration page, it works as expected and when checking received mail headers, it confirms the use of SMTP.
Edit: My bad, send mails with such settings is not using SMTP at all, but it uses drupal default mail system.
I'll open a new question for my needs.