No, but the privacy benefit is largely moot as soon as you send your query, which you have to do unless all you want to do is full-text search over your local cache. That's not really where YaCy excels, although it does support a number of complicated formats grep can't handle.
What YaCy provides is a DHT protocol for distributed keyword search. It has the potential to solve the biggest problem with replacing existing web indexes: lack of Internet Archive class bandwidth and storage. In fact, YaCy seems to do it quite well. It is a great step up from the Common Name Resolution Protocol and HTML-form assisted HTTP querying.
There is still much left to improve, with ranking being one. But client-side ranking provides benefits already: customization beyond what Google allows you to do in it's believe that it knows your interests better than you do (and in what language you prefer your content, solely based on your location).