You have 5 types of overlapping letters to that can be sent to a medical admission committee
Updates: new info you want to make the committee aware of. The information should be worthwhile and significant. Some schools encourage these buy many schools discourage or list policies not accepting updates.
Thank you: after interview
Letter of Interest: Typically, a post-interview but pre-decision letter that can reiterate and reinforce the school would be a good fit, usually with information you learned from your interview. This usually does not include a promise to attend if selected.
Letter of Intent: Typically written by applicants who have been accepted by one school but are on WL at another preferred school, outlining the reasons why you prefer it. There is little to scant evidence that these are particularly effective. It should be noted these are thought to have even less impact for those who are just on WL.
I will add one other type that is rarely used any more, the Reconsideration Letter: This is an applicant rejected pre-interview who has a large anomaly in their academic background that can be viewed through mitigating circumstances and asks to be reconsidered. With the non-screened/minimally pre-screened secondaries, there are plenty of opportunities for an applicant to express these circumstances.
To answer your specific question, there is no general prohibition against sending pre-interview updates. However, you need to read each school's website carefully and see if there is any indication that they encourage or discourage updates. I should also add that the way schools first screen, then evaluate application before passing it on to adcom review, how each will now take in and review updates varies widely. There really isnt a typical place that updates get read and noted on the application summary sheet, so how effective any will be is will vary widely. This is more the reason that a large fraction of schools dont encourage updates that anything else.
Updates should be short, very very short. In my opinion, I believe that you should be able to mention 3 "short" items else it really isnt worth sending. Or 1 or 2 big items
"I would like to update the admissions committee on my recent application now under consideration. This past spring and summer, I made a 3.7 GPA in over 20 credits, thus completing the requirements and earning my bachelor's in biology from University X. In addition, I have recently begun a position as a research assistant in a WHATEVER lab/facility. Lastly, I am continuing my volunteering/activity/etc in WHATEVER."
Thank you for your time and my appreciation of my candidacy to your school.
(if you have a demonstrable reason to mention why the school would be an excellent choice to attend or match for you, say it. This would be state resident, connection to the school otherwise, family in the area, but dont, repeat dont, go say the asinine thing along the lines that the school is your top choice unless you have a strong piece of evidence as to why) If it is an instate school, something along the lines of I would like to reiterate my strong desire to remain in the state. School X will provide both a great education preparing me for residency and medical practice with significantly less debt than other schools
