Yes, but you'd want to do that in After Effects. You could make a face in CH, drag it into an AE comp, and then use motion tracking to attach the face to a tracked point on the face, like an eye / freckle / etc. I did something similar here: https://www.instagram.com/p/poxYj9mTgX/
If that's new to you, check out YouTube for "after effects motion tracking" and it should teach you the basics. It's a really powerful tool, I use it all the time.