Yes. That’s how it would work. You need some hardware that directly generates such a stream though. So HLS, RTP or raw UDP.
If it wasn’t HDMI input but something like the Pi camera, you could even use the Multicast Video Streamer Package to generate such a stream. Thinking about it, it might be possible to use that in combination with this hardware encoder that (from what I understand) behaves like a Pi camera: https://auvidea.com/b101-hdmi-to-csi-2-bridge-15-pin-fpc/