With the SDI G2 model camera, the audio will embed over the HDMI and network only, but not over the HD-SDI. 

With the USB G2 model the audio will embed over the USB and the network, but not over the HDMI. A microphone directly into the audio line on the back on the camera will not work.

A microphone needs an amp to function and control it's level, the camera does not have any kind of amp or preamp to handle a mic level signal.