I completely agree with @notjoe’s advice, but I would like to add these thoughts:
Harvard has never published the number of students they have waitlisted, but Yale and Princeton have. In years past, YP have waitlisted about 2,000 students each. Of that number, about 1,200 to 1,300 students choose to remain on the waitlist at each college. I imagine Harvard’s numbers are the same. That’s for about 30 slots in a good year. You do the math.
There is literally nothing you can do – aside from remaining on the waitlist – that would increase your chances of being taken off the waitlist. That’s because Admissions has already built their class and IMHO will be seeking like-kind replacements – someone from a particular state/area/nationality, who is of the same gender and who has the same interests, so they can keep their state/gender/interest mix the same.
For example, if Admissions admitted a female student from India who declines their offer, they are going to go to the waitlist looking for another student from India who has the same interests and is of the same gender. In that case, if you’re a female international student from India with the same interests, your chances of getting off the waitlist are very high. But, if a female student who has an interest in Humanities from Texas (or any of the other 49 states) declines Harvard’s offer, your chances as a male international student from India interested in Computer Science are not good at all.
So, go ahead send a letter, tell Admissions what you can contribute to the campus, tell them what Harvard can provide that the college you are going to matriculate to can’t. In my mind, it won’t make one bit of difference, because now it’s completely dependent on who declines and if the stars are all aligned in your favor.
Send the waitlist update letter and then forget about Harvard. Waitlisted students must accept another college’s offer of acceptance, as Harvard will not start going to their waitlist until mid-May, several weeks past the deadline that every college has for accepting their offer.
Every waitlisted student needs to fall in love with a college that fell in love with them. If Harvard comes calling somewhere down the line, that’s great. If not, it’s their loss baby!