Yes, they will, but in a limited fashion. Volume wll work, play/pause will work, and the back and home buttons will serve to exit the Chromecast app. Not sure about shittle operations, have to try it. I don't cast often though.
Your TV remote will only work if you're passing commands via CEC.
During casting, the remote is whatever device you are casting from.
I don't have Shield, but on my AndroidTV, when casting from phone, the TV remote doesn't work