Usually the standby list goes to gate control at around the 1 hour mark. At this point, nobody but the GAs working the flight can add you to the list.

But as far as I know, the GAs can add people to the standby list/clear people onto the flight right up until departure (and even after in some cases!), though theyare usually too busy trying to get the plane out and may not be helpful in actually doing it.

One time I had a GA just tell me to board into a seat after boarding was complete. She never added me to the standby list and I never had a BP for that flight. Once the plane pushed back, she squared it away in the system (or possibly right before so the planes paperwork was correct, but I never got a BP)