No more or less than sending age information or registering an ID does. In all cases they must track content classification at some granularity (individual resource, single page, subdomain, some other scheme) and act on that information. The only thing that varies is how they act.
Yes, when it's client-sent they can hide classified parts of the page. When it's server-sent you either mark the whole website 18+ or you hide 18+ content for everyone.