Does WhatsApp backups count against my quota of my Google Drive?
Starting from November 12, 2018, the answer will be
Important: Starting November 12, 2018, WhatsApp backups will no longer count towards the Google Drive storage quota. Furthermore, WhatsApp backups that haven't been updated in more than one year will be automatically removed from Google Drive storage. To avoid the loss of any backups, we recommend you manually back up your WhatsApp data before November 12, 2018.
From Google Drive APIs: Storing Application Data
The 'Application Data folder' is a special folder that is only accessible by your application. Its content is hidden from the user, and from other apps. Despite being hidden from the user, the Application Data folder is stored on the user's Drive and therefore uses the user's Drive storage quota.
Your backups will use your Google Drive quota.