Supplemental LOR from a VIP?

There were a lot of similar threads on gmatclub when the first round wait lists went out. I'm speaking out of my ass here but I'd think that it partly depends on the school. H/S/W reportedly get a ton of these and they are supposed to mean little or nothing unless H/S/W can tell that the VIP knows you somewhat and is truly vouching on your behalf. If we're talking a Duke/UVA etc then who knows, maybe it would tip the needle.

One example that I read (somewhere) was about somebody who had a family connection to the dean of admissions at either Stanford or HBS (I think Stanford). The dean agreed to write them a LOR but pounded the point home that they would have to completely recuse themselves from the acceptance decision for that candidate. As you know, Stanford puts together a very hand selected class so taking the dean out of that decision making process was in and of itself a huge handicap. The point was well taken and I don't believe that the individual elected to go that route.

Of course, history has surely seen exceptions.

To your final question, yes, I would say it is unprofessional to outright ask for a letter if you do not know this person well - especially if it is a first introduction or one being made after you've already been wait-listed. Just enjoy the opportunity to meet this influential person, walk them through where you are and then ask if they could suggest any additional steps. They'll come out and offer if they're willing.