Yes that is possible, but in the past it has been very rare that that happened. Mom may correct me but i can only recall one year that they ran out of visas in total and some AOS applicants in the end of September lost out. There have been a couple of instances that individual country limits were reached but in those instances even CP applicants had interviews cancelled so even that is no assurance. (There is no “regional hard limit” as you imply btw, it’s only country limit or total visas where they cut off.) Unfortunately while there are many advantages to AOS, this is one of the drawbacks you have to accept when doing it, you can’t force a FO to bring your interview forward because you’re worried they’ll run out of visas.
Btw I don’t know (because I haven’t been following developments closely recently) where your 34k number comes from, but your math is a little out because there are 55k visas available so there is room for another 21k visas/green cards, not 16k.