Can I add my own CSS styles that don’t use the Style builder?

Yes. You can add your own styles to a sub theme.

Acquia Cohesion includes it's own Drupal theme called "Acquia Cohesion minimal theme" that provides the basis for the theme you create using Acquia Cohesion's style builder and template builders. You can add your own stylesheet by creating a sub-theme if you want to develop additional styles by hand.