Theme Simplenews with MailSystem
You do have the template files in themes/bartik*? Make sure to rebuild the theme registry.

This feature is relatively new but we've used it several times for ourself now and have multiple confirmations from other people that it works for them.

Note that the only thing that "using a theme" means is the place where Simplenews looks for the template files. Additionally, Mimemail also looks for for either the css files to embed or the mail.css (Hint: Older versions of Mimemail have their own setting, switch to the most recent dev version of Mimemail to get that fixed).

It does in no way take over the look and feel of your website, if you're looking for that, have a look at HTML Mail.

*Hint: You should not alter a core theme or add files into it, instead, create a subtheme and put that in sites/all/themes. Try Google to find more information about subthemes.