I was really hoping you guys could possibly figure this out. I think it would be really cool.
It used to be possible before netflix switched to html5. It now requires a paid codec that isn't added in the default package of the chromium browser because of legal bullshit.
I looked into it before and it would require me to basically compile chrome from scratch.
For now you could use the alt+3 feature to make a clone overlay from netflix in your browser.