There is absolutely no evidence that such letters move the needle, anywhere, before you have an initial decision. They certainly will never turn a R into an A, and, of course, they are unnecessary if you are going to receive an A anyway. It will also not serve as a free pass off the WL if that's where the adcom has decided to send you, since at this stage you are being judged by the strength of your application rather than by the intensity of your desire to be accepted.
There is, however, anecdotal evidence, plus advice from some adcoms who post on SDN, that LOIs can be effective in moving you off a WL later in the cycle, since at that point the school has already made a determination that it would take you if it had space, and you are indicating a commitment to attend, which they love when pulling from the WL. Of course, if the WL has an internal ranking that is undisclosed, sending a LOI if you are low on the list won't help, but you won't know that, so you should send it anyway and see what happens.
Bottom line -- sending one pre-decision will never have the desired effect and will just come off as desperate, which could hurt later on. As difficult as it is, the only thing to do at this point is wait for a decision.
