Cache tags for anonymous user with internal page cache?

Is it possible to change an array value dynamic (with Internal Page Cache) for anonymous users with the usage of cache tags?

The documentation says no: Internal Page Cache

But this documentation (Cache Tags) says: «Comprehensive use of cache tags across Drupal 8 allows Drupal 8 to ship with its Internal Page Cache enabled by default.»

What i want
i want to use the cookie data to create custom classes in a twig template (page.html.twig).

So i have tested this:

<?php
function mymodule_preprocess_page(&$variables) {
  $variables['#cache'] = [
      'contexts' => array('cookies:customCookie'),
      'max-age' => 60,
    ];
}
?>

This works great for authenticated users but not for anonymous users.

My question
Can i use cache tags to make this also works for anonymous users without having to disable the Internal Page Cache module?