Comment count unpublished
I don't think there's anything already in page.tpl.php but it really depends on what is happening in the preprocessor(s) of your theme. I don't know what theme you're using.

If you're worried about calling a function like comment_count_unpublished() multiple times in one page load why not statically cache the result with drupal_static()?

Have you actually profiled that query and shown that it will cause problems on your site? Drupal generally runs hundreds of queries each page load so I don't think counting the unpublished comments in that table would have a noticeable impact on most sites.