It won't hurt you if you're not, but it does help if you are. Top tier programs tend to be top tier programs based primarily on research. The USNews ranking are heavily based on NIH funding to the institutes, meaning top tier programs are top tier because they are heavy into research and receive a lot of funding (good number of RO1s, PIs of large multicenter studies, etc.). Thus when you look at those residencies classes, there tend to be a larger proportion of MD/PhD at those programs. I'm not saying you have to have a PhD to get residencies there, but I would suspect that research productivity holds more weight than AOA status. Just my opinion, some one else is welcome to say otherwise, as I have been at a couple of top tier programs, but never on the resident selection committees.
Just as a caveat, know that some medical schools don't offer AOA status to students because grades are pass fail (Havard is an example).