Totally depends on the school, the ADCOM, and (least importantly) the person recommending you. Once you're on the wait list, plenty of things can tip the scales in your favor, or totally against you. Anyone who makes an unsolicited call or sends an email further recommending you might help. I've been told this by professors and academic advisers who thought they were "nobody" but received emails in response to their "extra support" that said "thank you for helping us make a decision" as the student received an acceptance. ADCOMs are composed of normal human beings who are often at a loss as to who to choose among a group of equally compelling candidates. You might be a member of one in the next few years. How do you decide? You have to choose from students with basically the same scores, great ECs and LORs, and their interviewers really liked them. What tips the scales? Put yourself in their position. You'll get sick of candidates who "update" you biweekly, when they have nothing to say. But when something sends an unsolicited letter of intent, and the person who supervised their volunteering or research for 4 years emails or calls you to say "you really should take him/her, and here's why, in addition to what I already told you," wouldn't you consider this student above others? After all, part of admissions is accepting people who choose you first--it's an unofficial match game. Few professors are going to call the 30 schools their research student applied to, so a simple call or email might really make a difference.