From the tutorial, http://www.howtoforge.com/how-to-speed-up-drupal-7.7-with-boost-and-nginx-debian-squeeze-p2 Does it work on Drupal 6 ?
Basically yes, since there's a Boost module for Drupal 6 as well, but it is possible that your Apache rewrite rules differ, and maybe you also need a different nginx configuration (take care about the extensions where nginx should deliber a 403 forbidden - these might be different for Drupal 6).