I interviewed at about 58 programs in 3 specialties. I would say the majority of my thank you notes were responded to - some generic responses some more specific. I can't tell you that they had an impact - but I did end up getting at least 10 "you are at the top of our list/ we are seriously considering to rank you, etc. type e-mails"
-But I would think the greatest impact would be from your application (USMLE, MSPE, grades) and interview.
-if the thank you note did have some impact I would imagine it to be very small
-the only way to really get an answer is to do some survey for each specialty for PD but apparently the responses from the PD and administrators here at SDN is that they don't mean much.