I think you're asking if it's possible for your government to be a man-in-the-middle? Depending on which government you live under, the answer is likely no but more importantly the answer will always be; it's not worth their effort to find out what you're watching.
YouTube's public key is signed by a certificate authority whose public key (root) is likely installed on your device from the factory. When you connect to YouTube, they send you a certificate chain which your browser will verify against that known root. In effect, it's information both you and YouTube already share and can't be tampered with over the wire.
Technically, those signatures can be forged by a well resourced adversary (i.e. a government) with access to the certificate authority through subversion, coercion, etc. At the same time, it's probably easier to subvert or coerce you or YouTube to reveal what you watch.