Yep, I discovered this method yesterday and it's working.
Thanks for your confirmation.
You just described what streaming is for. That's how OBS is designed in general and its main purpose. Use its streaming function. OBS is a streaming client that composites video+audio, streams it to some streaming service you choose, and consumers can tune in to the streaming service and retrieve that stream.
You can use restream.io to broadcast simultaneously to multiple streaming services.