Does PieSync sync with CardDAV data stores or have an open API?

We do not presently have an open API.
CardDAV is a way of storing and accessing data that's specifically built for contact data.
It can be used by different tools. iCloud, for instance, uses that protocol.
Although PieSync can technically connect to a tool supporting CardDAV, as we support iCloud, we cannot freely connect any CardDAV data store or application relying on CardDAV.
Similarly, we currently don't support any free-form applications, such as Google Sheets.
If you'd like to learn more about syncing contacts with Google Sheets, take a look at our blog on "The guide to syncing contact data with Google Sheets."