Can I use Google CardDAV sync on my Mac?
Correct me if I'm wrong, but it seems like CardDAV sync feature is only avaliable from iOS devices. I did however find an article showing how you can do so on your mac, it could be worth a try.


  After opening Contacts, go to the app’s preferences pane. Navigate to
  the “Accounts” section:
  http://ismh.s3.amazonaws.com/2012-12-16-google-contacts-1.png
  Hit the plus sign to add an account. Here are the required settings:
  Account type: CardDAV:
  Username: Your Gmail Account
  Your password
  Server address: google.com
  
  Hit the “Create” button:
  http://ismh.s3.amazonaws.com/2012-12-16-google-contacts-2.png
  Contacts.app will then ask if you want use these credentials for other
  types of information. Select what you wish and press the “Create”
  button again.
  
  Once the account is listed in Contact.app’s preferences, go to the
  “General” section and set your Google account to be the default
  account:
  http://ismh.s3.amazonaws.com/2012-12-16-google-contacts-3.png
  
  By default, the application defaults to saving vCards locally on the
  Mac, which means information added from other programs won’t end up in
  the Google cloud.