Is it possible to have WordPress not recognize category URLs?

Look at the code @scribu suggested for a function unregister_taxonomy_from_object_type($taxonomy, $object_type) (the last patch currently).
Until the code has found its way into the core, add it to your functions.php, wrap it into a function_exists() and call it on init.

unregister_taxonomy_from_object_type( 'category', 'post' );