I don't think this would be seen as fair to the other candidates and I would discourage it. It could be perceived that you're expecting special treatment and that would probably negate any benefits of showing interest.
The more critical orientation to have right now is amping up *their* interest in you. So if there is something you can share with them that would increase your perceived value that's what you would want to do. If you improved your test score or if you got a promotion or even if you received a promotion in the area of community service.
I recently helped someone get off of the waitlist for INSEAD the month before school started and the only real update he had was being promoted to the manager for the local soccer club. So thank broadly about potential updates.
If you have some good updates to share then it would be appropriate for you to plug that in but I think making that the sole focus of the communication would be a little tacky borderline Primadonna.
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