Yes, they do 'work'.
Not only do they prevent stiff neck problems but improve belaying skills in my view by increasing my ability to closely watch the leader at all times. Without the glasses I am unable to tilt my head backwards to look up at the leader for the whole length of time that the route takes.
O.K. They may not be cheap but neiher is a course of physiotherapy!
I paid £85 for my glasses.