No, CatchApp does not sync with your Google (Gmail) contacts. CatchApp syncs with the contacts on your mobile phone and is able to send invitations to both email addresses (via email) and mobile numbers (via SMS).
If your mobile phone is already synced to your Google account, then you should be able to see those contacts inside of CatchApp.
In the future we do plan to include a direct Google contacts integration that will allow you to import all of your Google contacts to CatchApp.
If you have any questions about this, please get in touch using the chat button on the bottom right of the screen.