Can MySQL 5.6 be used with Drupal 6 and php 5.2.17
MySQL 5.6 works fine; using the mysqli driver. PHP 5.4 works after fixing a couple of notices, and php 5.2 works without any modifications.

In your settings.php file change $db_url = 'mysql://...' to $db_url = 'mysqli://...' to use the mysqli driver; it's that simple.