If done the correct way, it can boost your chances. Before doing so, make sure you are serious about the school. The *best* way for it to work is for you to send a letter to the dean, and another letter (same content) to the dean of admissions.
State that the school is your top choice, why it is your top choice, and why admitting you would benefit the school (this part is key). Also state that, upon admission, you will pay the deposit right away. Obviously, in order to state this and be truthful, you have to be serious about the school.
This works in part because schools like to see dedication and perserverance on the part of the applicant, and they enjoy knowing what you can add to the school (both as a student and alumni).
This method also works well because schools participate in the admissions crap-shoot in the same way that students do -- that is, they send out many acceptance letters knowing that only a certain percentage of those students will commit to the school and pay the required deposit. If you are honestly assuring them that you will do this (and do it quickly!), then it gives you another added advantage.