So, I wrote something like an LOI after ranking had been done, and while I can't definitively say how much it helped, I can definitely say it helped me get in sooner. It's kind of a funny story, but not something I can disclose on a forum here. If anyone's interested after quartiles come out, shoot me a PM and I'll give you some suggestions.
I'm torn on how LOIs are perceived. I think that just giving updates in general tells the school that you're interested, and that's really all you should need to do. An LOI isn't anything shiny or special because what's to stop people from sending them to every school they interviewed at?
That sort of decision is up to you. I don't think it will hurt you if you do, but I don't see how it'd help you any more than just a quick update.