You could get a vector of the position of the camera to the position of the object and project (dot product) that vector along the transform.forward vector of the camera. If the result is positive, the object is on the front side of the camera and if its negative its behind the camera. Still, if it is positive it does not guarantee that the object is visible due to the camera frustum but you could combine this info with the screen info you got previously and have a pretty good estimate of when an object is visible or not.
hope it helps
