The ad data (text, layout, media) can still be hidden on the client, but AFAIK with QUIC you can push it to the browser regardless if it actually was requested.
You might be thinking of the HTTP server push functionality. That was introduced with HTTP/2 and has been deployed for years already over TCP transports (i.e. totally unrelated to QUIC).
Due to how advertising networks work, I'd be surprised if anyone used server push in the way you fear.