Do the eyes of geriatric patients turn paler in color?

Possible. There can be some change towards lighter iris color in the elderly. Also, corneal changes called arcus senilis can make the outer portion of the iris appear to be getting lighter colored or white in appearance to a casual observer. None of these changes affect the patient's vision.
They may seem to. It is possible that aging can cause a reduction of the pigmented cells of the iris, making the color of the eye appear to fade over time. However, more often, the cornea (window) of the eye can become partially opaque, especially at the edges, and make the pigmented structures of the eye behind it appear paler. Most of the time nothing to worry about!