Yes, it's possible. Some sports broadcasts do this. The ones I'm familiar with use a high pitched tone on the edge of human hearing but still audible to most people.

Streaming services watermark the video as opposed to the audio as I understand it.

But that's for tracing pirated content back to the originating user account. It's not particularly useful (also entirely unnecessary and overly complicated) if your goal is to ID a piece of content as opposed to an account.