hey there, as an MS-II, I can still clearly remember how nervous I was throughout the admissions process, so I thought I would chime in with my personal experience.
After I interviewed at the school I currently attend, I wrote up a "letter of interest" one week after my interview (the admissions director had told us on interview day that it would take ~3 weeks to make an admit decision following the interview.) The format of my letter was informal (simply a date at the top, "Dear --- Admissions Committee", and "Sincerely, [my name]" at the bottom), but the language was formal (expressing my thanks for the interview opportunity, my preexisting ties to the school's neighborhood, three reasons I wanted to study medicine at the school in that particular city, and my intention to accept an offer of admission if made to me.) Since I didn't live very far from the school (just a 20min drive), I decided to hand deliver the letter on a Friday afternoon. I dropped off the letter with a secretary in the office and informed her that I had already been interviewed at the school and wanted to express my thanks to the committee.
I received an acceptance letter exactly two weeks later (just as the admissions dean had promised we would receive a decision w/i 3 wks.) I'm not sure if the letter of intent helped played any part in the committee's decision to accept me, but it definitely didn't hurt as I was accepted.
My advice based on personal experience: as long as you are courteous, gracious, and non-arrogant (i.e., not-too-pushy) in all your interactions with the admissions committee, they will welcome things like 'thank-you notes' and a 'letter of intent'.
One last suggestion: If you have not yet received an interview by Jan/Feb/March, and think you really deserve one, ask your pre-med advisor or undergrad recommendation committee head to see if they can shake the tree on your behalf. Sometimes, depending on how late you applied, your application can get 'lost' among the hundreds/thousands of other well-qualified applicants. Based on what I've heard from docs at my school, a call from someone known to them on your behalf can help you get noticed in the midst of a busy application cycle. At most schools, as long as you get your foot in the door of that interview room, everything else besides your personality and formative experiences melt away to the background when it comes time to decide whether or not they would be proud to have you as a student, future colleague, and ambassador of their school's reputation.
