This is an interesting idea. However, for a noise box to be effective requires that a significant number of people are also using a noise box, which assures plausible deniability the same way TOR and shared-IP VPNs do.

If you're the only one using a noise box, or are part of a very small minority of users that do, the random noise you generate is just increasing your attack surface through which the government can more easily target and identify you.