You definitely will get a red beep for a documents check. Using online check in and self printing of boarding passes doesn't stop CX from checking your documents. It's happened to me multiple times.
Yep, though when the document by its type and past verification allows access to HK, it might be a simple formality or no beep at all.
Whereas a documents check at manual check-in will raise the nasty "check-in of the final leg" question. Formally, at JFK, with only check-in until HKG, access to HK is to be checked. And with a HK passport and maybe a UK passport, that could be fine, without onward journey.
Or maybe cancel the lucky ticket, being not that lucky at all. 🤕