We have a deer problem in my area, and some people like to use the whistles. There's no way to know for certain if they prevent any accidents, though they certainly don't prevent all of them.
Personally, I don't think the problem is that they can't hear you, or aren't aware of your presence. The problem is what they choose to
do with that information.
Some are so accustomed to human presence, they choose to do nothing and you have to wait for them to cross the road in a leisurely fashion.
Those that do choose to flee are hard-wired to bound off in unpredictable directions to escape predators. This works great if you're fleeing a wild dog, not so much when you're dealing with hundreds of pounds of metal and plastic going several times faster than a predator can run, and only capable of going in a straight line and following the hard grey ribbon on the ground. Evolution hasn't caught up with the environment.
And then there's the famous "deer in the headlights" response at night, where they're quite aware of your presence but probably think they're staring into the eyes of god himself or something....
The only deer avoidance system that is going to give us any hope of avoiding the critters is the one between our ears.
edit: the only time you'll hear whistling coming from my direction when I'm on the bike is when I pass a pretty woman
, and had one deer hit me in the rear quarterpanel above the tire 
. I guess it was dark...
