You would only get two channel downmixed lossless over coax or multichannel lossy (e.g., DD, DTS).
Since I have a 2 channel home theater set up, I use the arrangement you are suggesting with HDMI to my Panasonic Plasma for video and coax to my EMM Labs XDS1 for audio (lossless 2 channel).
Since I have a 2 channel home theater set up, I use the arrangement you are suggesting with HDMI to my Panasonic Plasma for video and coax to my EMM Labs XDS1 for audio (lossless 2 channel).