I wouldn't be surprised is AACOM gave that information to schools. I would be surprised if adcoms used that info or took it into consideration when determining whether to grant an interview or not.
What would having a long list mean? You want to be a DO? They kind of already know that.
What would a short list mean? You have strong stats or just can't afford to apply to a lot of places? They would know that anyways as well. I don't see how it would be particularly meaningful.
UNECOM is an exception here. They explicitly ask you to list all the medical schools you applied to (DO, MD, and international) in their secondary.