No it wouldn't help if you're expecting them to simply shift you to the top of the waiting list just from one simple phone call, if that's what you're implying. And no, that was not what I was saying if you read my post.
If you miss the cutoff, you miss the cutoff, and if you read what I posted above, I was referring to speaking to someone who is aware of the system and someone who is part of the decision-making process, and someone who can give some real advice (for eg. alternative entry such as transferring, as I mentioned above) as opposed to someone who just picks up the phone at the reception desk and can just give immovable "yes" or "no" answers, more or less. By 'admin people' as I said above, I'm referring to the admin people who answer the phone.
Speaking from the perspective of someone who has worked as academic staff and having also been involved in a coordination and decision-making role at a top tier university, I know not only what the hard and fast rules are, but also the read-between-the-lines bend-the-rules circumstances that can sometimes, on the rare occasion, happen behind closed doors. And all I can say is, it doesn't hurt to call and if you're able to get the right person, even if all they can do is give you helpful advice for next time, it's worth the call. As I said, they may remember you the next time you want re-apply or transfer.