$comment_count

From what I could see, seems that cant access to the $comment_count variable in the user profile page.
Also because the comments output is taken as #markup and not as an array.

I think we can just add 'comment_count' => $profile_comment->comment_count, in $account->content['user_profile_comments']array and under the user_profile_comments_user_view($account) hook

That becomes like this:

  // Add user profile elements.
  $account->content['user_profile_comments'] += array(
    '#type' => 'user_profile_category',
    '#attributes' => array('class' => array('user-profile-comments')),
    '#weight' => 5,
    '#title' => t('Comments'),
    'comment_count' => $profile_comment->comment_count,
  );