There is the GData plugin which periodically pulls in GMail contacts, and adds them to Claws Mail's address completion list. That means that even though they're still not in the addressbook, they are available in address tab-completion when composing emails, or in filtering based on address book.
It's not a real sync, but it's something that happens automatically in the background, so it might be more comfy than a manual import. Personally, I added an action in Claws Mail to open GMail contacts in a browser, and I just use that instead of the built-in addressbook.
Claws Mail cannot directly sync gmail contacts.
There is the GData plugin which periodically pulls in GMail contacts, and adds them to Claws Mail's address completion list. That means that even though they're still not in the addressbook, they are available in address tab-completion when composing emails, or in filtering based on address book.
It's not a real sync, but it's something that happens automatically in the background, so it might be more comfy than a manual import. Personally, I added an action in Claws Mail to open GMail contacts in a browser, and I just use that instead of the built-in addressbook.
(Full disclosure: I wrote that plugin.)