CatchApp for iPhone
No, CatchApp does not sync with your Google (Gmail) contacts. CatchApp syncs with your contacts on your iPhone and is able to send invitations to both email addresses (via email) and mobile numbers (via SMS).
If your iPhone is already synced to your Google account, then you will be able to see those contacts inside of CatchApp.
CatchApp for Outlook Email
Because you are using CatchApp inside of Outlook email, you will have access to all of your Outlook contacts.