That's the difference between a letter of interest and a letter of intent. Both are sent after an interview and before an acceptance.
In a letter of interest, you're providing reasons you think you and the school are good fits for one another, and restating your interest in attending the school if admitted. As
@Goro has explained, though, these are pretty useless: the fact that you submitted an app and attended an interview already indicates your interest, so reaffirming it in a letter doesn't tell them anything they didn't already know. Moreover, a letter of interest makes no mention of any other acceptances so it really doesn't have much weight -- the school has something you want and they have tons of great candidates, and if you're not admitted anywhere else they can string you along all they want. To be frank, if you're writing a letter of interest, it means the school has all the power in the relationship and you have none.
With a letter of intent, on the other hand, you're basically writing a letter of interest and adding, "If you accept me, I promise I'll attend." If you don't have any other acceptances to dangle in front of the school, however, they still retain all the power. But if you mention that you have other acceptances, you take back a little of the power: you're saying, "Oh, BTW, I've been accepted elsewhere so I'm not desperate. Love me now or lose me forever." That mention of other acceptances is the only way a letter of intent has any power.
Look back through the post history and read gonnif's words that Goro quoted. According to gonnif, there's not much evidence that letters of intent work, but if they do it's because the candidate had other acceptances and therefore the ability to walk away from the school.
To answer your questions:
As gonnif said, unless you hold the trump card of another acceptance, it's really not persuasive.
Totally.
No, they won't do that. Schools don't do pity acceptances, which is essentially what that would be. They're not running a charity to make people's dreams come true. They're trying to pick out the best candidates from a phenomenal pool, and they're competing against one another for the best ones. By mentioning other acceptances, the candidate makes the school pull out its waitlist and say, "OK, we have to decide whether to take this applicant or pass, because they're no longer completely at our mercy." It's an attempt to force the school's hand: if it wants the candidate, it has to act because otherwise the candidate will walk.
That's
exactly what people are trying to do by sending these letters. The problem is, schools have so many great applicants that they can generally say, "OK, cool, see ya," and they've in fact lost nothing. That's why gonnif says LOIs aren't particularly effective.
