I've seen a programmer-turned-streamer literally do this live. Woohoojin on twitch/yt focuses on content for Riot's Valorant esports title, during a couple watch parties he would make "super fans" using GPT with TTS output and the stream of chat messages as input. His system prompts were formed exactly like yours, including instructions to plug his gaming chair sponsor.

It worked surprisingly well. The video where he created the first iteration on stream(don't remember the watch party streams he ran the fans on): https://yewtu.be/watch?v=MBKouvwaru8