Does Screen Sharing also share the audio of a video I am playing?

Can my client hear the audio from my browser/computer when I share my screen?

Yes! Screen-share has the ability to share audio with your clients however Chrome is the only browser that supports this feature at the moment. 

To do this, ensure you have the video/audio open in another Chrome tab. Then Start Screen Share and select Chrome Tab:

Ensure Share tab Audio has been selected & hit Share: