I never tried to do an core update on the command line. Today I tried it.

Get the latest drupal version

drush dl

Check your download

ls
drupal-6.x

Checkout svn drupal-6-core

svn --username=build2be chechout http(s)://my-svn/drupal-6-core/trunk/

Step into drupal version to update

cd trunk/www

Apply the patch

diff -ru ./ ../../drupal-6.x/ | patch -p0

Is this all?