Not from CH (yet), so you'll have to go through your own system's audio.
So in OBS, for example, I select the microphone as my audio source and give it an 150-300 ms delay in the "Mixer" area, which worked for the "Red Monster Live" video we did (I talk about it about halfway through). Red Monster Live! (Adobe Character Animator Livestream) - YouTube
For PC solutions with Newtek's NDI plugin, like Wirecast or VMIX, you can try the same idea. Or we've used NDI's Scan Converter when using multiple audio sources, like the multi-puppet livestream we did: https://youtu.be/ja7bVr4kHCU?t=15m22s
Hope that helps a little...
So i just downloaded OBS is there a way to stream the video/audio out locally through HDMI to another monitor with speakers? I'm wanting to give a live performance and not have to go through a source like twitch/youtube/facebook. Any help would be great! Right now when i livestream locally only video comes out and when i run sound separate the audio sync is way off.