Is it possible to pass parameters in a taxonomy term's aliased URL using clean URLs?
Yes, the arg() function can do this.

https://api.drupal.org/api/drupal/includes%21path.inc/function/arg/6.x

At the end of Drupal's .htaccess file, you can see how Drupal makes those URLs work by rewriting them to ?q= if they are not real files or directories. Without this, they would cause a 404 too.

In http://api.drupal.org/api/function/arg/6 you can see how it handles them.