My understanding from GAs if there's open seats the GA has latitude in when they can start to process upgrades. Some will process them immediately while some will wait to near boarding time. Where they don't have latitude is when someone with an F seat hasn't checked in yet. I believe the system locks them out on processing that seat(s) for upgrades until about T-30. Despite online check in there's no shortage of people showing up at the airport at T-40 heading over to a kiosk to check in.
However, in the case of the latter where I've been number one on the list and someone hasn't checked in the GA will sometimes call me to the podium and ask that I don't board because at T-30 they will have a seat for me. I had one GA at PHX actually call out a count down to me.