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.

That's not necessary. If a service has access to the raw audio of a show, it can fingerprint each second of that audio in a way that can be matched in a tiny amount of computation even for a recording in a noisy environment.

That can't recognize what you say. But, it can ID where you are in a specific show out of zillions of hours of shows.

Honestly, it doesn’t even need to be outside the range of human hearing.

A quick search for “audio steganography” should answer your question (and be a fun rabbit hole if you find that sort of topic interesting)