I'm not too familiar with the comment system in Drupal, but you should be able to.
First check that the commment admin page is loading the theme you are using and not a system admin theme (Link to a screenshot if you are not sure).
If it is loading your custom theme then inspect the elements that you want to wrap as you may already have unique classes that you can use to style. Even the body tag should have unique classes for the comment admin section or you could add unique body classes in the template_preprocess_page function in template.php
If it is loading an admin/default theme you have 2 safe options:
Set drupal to load your custom theme for admin pages (but then you would have to style all the admin pages)
Copy & rename the admin theme, and set Drupal to load the copied theme for admin pages and change the styles in the copied theme.
If you know PHP well enough you could add your own template but you would have to override the default Drupal hook - hook_comment_admin_overview() and add a template to the form with the theme() function (if a template file doesn't exist) but that could be quite difficult to get working without breaking.
Finally, if all else fails the quick dirty way would be to add html wrappers with jQuery but this is not recommended.
Please check in your theme's html.tpl.php you have this code snippet:
<body class="<?php print $classes; ?>"
There should already be classes that are added to the $classes variable when editing a comment.