So I know sending LOI pre-interview invite comes off as desperate/uninformed. However, I am in a master's program which has a link to my state medical school. In the program, I took an elective taught by the dean of admissions (who attended some classes, did a mock interview, and graded assignments). So I'm not totally uninformed about the school and this is definitely my top choice. Is sending a LOI to the dean before receiving an invite advisable in this case?