Yes it's possible to build a full classification of cookies used on your website, provided that you know them. Indeed the component supports up to 4 categories that are fully customizable,

By default there are 4 preconfigured categories named as :
• Necessary – Cookies that could prevent the proper functioning of the website
• Preferences – Cookies that allow websites to remember user informations such as language, location, etc
• Statistics – Cookies that help website owners to collect and report informations about the interaction of visitors with the website and their data. This category includes Google Analytics and could track information anonymously
• Marketing – Cookies used to track visitors and to display ads and promotional contents

Moreover the site administrator can choose which kind of cookies should be blocked and the method to block cookies. Using component settings you can choose to:
• Block the technical/functional cookie related to the Joomla! session
• Block third-party cookies based on domains, so including/excluding statistics, marketing cookies, etc
• Allow certain technical/preferences cookies, for example to have Google Analytics working provided that you have activated anonymization to be compliant
• Activate the cookie block both client side and server side