Without IK, yes, it will follow the prop.  One would need to be careful not to translate the prop and make sure the prop moves with the body (etc. etc.).  Seems overly complex.

My thought is this:  If you don't mind an extra bit, add a prop near the camera.  PointAt the head to the prop (following PhilC's advice about the End Point!).  PointAt the eyes to the camera.  Now you have control of both the head and eyes.   This is a bit more piecemeal as you now have two
'controllers' (to the rest of the 3D world, this is the correct terminology), but you have very precise control of both movements: head and eyes.

C makes it easy to shoot yourself in the foot. C++ makes it harder, but when you do, you blow your whole leg off.

 -- Bjarne Stroustrup

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