Check if Drupal 7 region is empty and print a body class (template.tpl.php)

Add to your template.tpl.php the following function:

function YourThemeName_preprocess_html(&$variables) {
if (empty($variables['page']['RegionName'])) {
$variables['classes_array'][] = 'YourClassName';
}
}

Drupa API
7 – 8 template_preprocess_html(&$variables)
http://api.drupal.org/api/drupal/includes--theme.inc/function/template_preprocess_html/7