Don't have much insight on this but my hunch is close to nothing unless the adcom reading your file happens to know the letter writer and holds him/her in very high esteem or said letter writer is world renowned OMT pioneer.
This one doctor I shadowed finally decided to write me a letter. It was for one school that I hadn't finished the secondary for yet. Oddly enough, he went to that school many years ago. Also, it is a school in my state which is regionally biased (based on reading other posts on SDN). It was one of my long shot schools but I hope I have somewhat of a shot now
One should be careful when he or she decides to name drop. It can be done very artfully but takes skill to not come across as sounding like you are saying "pick me because I know XYZ who attended your school 123 years ago." There is always a chance that the physician will be remembered as someone no one liked as well.