On two occasions I have boarded and received a text that my upgrade has cleared. I called a FA to get me my new BP from the GA and moved seats. So I guess there is a system in place and perhaps its a lot of work for the GA.
Re the posts upthread that flights leave with empty seats - as per my experience specially on late flights, the supervisor explained to me that the flight was 'closed' so they could not process upgrades even though someone probably called the concierge and cancelled their trip. This was on a YYZ-LHR flight that was several hours late, well past midnight.