Every school is different.
Some rank candidates immediately, and just pull them off the list in numerical order. Other schools lump people into ranked groups, like "High priority" or "Acceptable", etc. I assume that in those situations they would go over all the candidates in the group before making an offer - it's in these types of waitlists that an LOI does the most good I think.
And still other schools reveal no information whatsoever about their waitlist.
I think overall, it depends on the school whether an LOI makes much of a difference. At the very least, it certainly won't HURT your chances at all.