Hi there DanPruett,

The simple answer is indeed Yes!

There are several things to consider:

1 - Teamviewer License
The Teamviewer free license is for home use only, ie using your home computer while on the road etc. Officially speaking you'd need to get a business license to legally use teamviewer for this purpose. However, no-one will stop you from using it other then a popup that you're trialing or home-use.

2 - Computer load.
I've found that Teamviewer does use up a significant amount of computer resources. We recently swapped to anydesk which seems to be lighter and also a bit more stable in terms of resources used.

Then to answer your sound question:
It all depends on how you set it all up. Basically remote desktop programs can send you on the remote side the desktop sound. So in order to monitor the sound you'll need to set up Vmix so that it sends headphones or master to desktop rather then a specific interface. Any video played within vmix will go to whatever bus you assign it to, so as long as your video has its sound turned on (or auto) when its playing on program, it should be in your livestream/website. If its not make sure to check if your mix one is using the Master bus as audio source.

The one last thing I advise against is using the built in windows remote desktop function. It does work, but when you connect, the host computer will actually reconnect its display/relog/reconnect devices when you log in and out, messing with your vmix.

Another option is Google Remote Desktop. It works well for me, better than teamviewer. You can try that and let me know how it works for you.

Maxi