The issue of thank you notes - whether, timing, style, etc is an unending one from med school admissions through faculty promotions. As the recipient of a huge number of these thank you notes (I interview at every level), I will just say that the letters USUALLY (almost always) have nothing to do with acceptance. What they do is further the connection between me and the interviewee and that is a good thing to do at all levels.
They are also evidence of politeness and respect for the time the interviewer spent. I don't get a dime (not part of my funding at all) for any of these interviews. It's not part of my faculty status/promotion (I am a full prof, can't get promoted). I do them because I like meeting trainees at all levels and interacting with them. It's among the most fun things I do - beats the heck out of hospital committees. Nice thank you notes are appreciated, but not mandatory.
I could care less how they are sent - email vs hand-written. Others might feel differently.