My answer is essentially the same as Bing’s.
While I can’t prove that they work, I have lived in a heavily deer-infested area for almost 20 years, and I have never had a “deer incident”.
By contrast, during that same time period a friend of mine has had two deer-related collisions on roads adjacent to my house when coming to visit me. The second of his deer incidents was relatively minor, but the first one resulted in the totaling of his like-new Honda because his car went into a ditch when his brakes locked up while he was in the process of avoiding the deer. He doesn’t use deer whistles.
I have noticed that, when deer are in a field adjacent to the road, they tend to turn and look in my car’s direction as I approach, but I don’t notice this effect when I drive other people’s cars that don’t have deer whistles. Again, this doesn’t prove anything, however.
I certainly can’t prove that they work, but just on the chance that they do, the extremely low cost of these devices makes them worthy of consideration–IMHO.