I was hoping it is possible to route analog audio from the RCA jack audio input on my HC800, using the audio encoder in the HC800 (assuming such a thing exists), to speaker points around the house. If so, how would I get that audio input to show up as an available audio source in the various rooms with speaker points? If not, how could I do such a thing?

You can, one would simply add a driver for that source (if you want to use it for a computer or a local 'plug-in' for a phone etc, a no - control driver could be used) into the system, it will show up without further 'work' everywhere you have 'C4 audio' available (meaning where you have a speaker point, or a controller feeding an amplifier or receiver).

However, note that it WILL cause a delay on the audio, and thus this will NOT work for video source.

Thanks! Definitely audio-only.