Even if the devices were effective, they would soon become clogged with insects and dirt (since they are mounted on the front of the vehicle) and would stop working.
The state police in Ohio, after months of testing, found no significant decrease in patrol car/deer accidents after the warning devices were installed. In fact, more accidents were reported by the officers after the whistles were installed than before for the same period of time and stretches of highway. Tests conducted in Utah, Georgia and Wisconsin also concluded that deer whistles don't work.
The odds are you won't hit a deer. Your best protection is to drive defensively, particularly as the sun sets. This is when most vehicle/deer accidents occur. Slow down when you see one deer. More often another is right behind it.
Read more here, from the Washington State Univeristy:
Some tips on avoiding accidents with animals: