Originally Posted by BullishGS

Gate agents can certainly add your companion to the list. If you're at a station that has a GS reception, you can also ask the GS agents there to add them to the list.
Nowadays most airports have the new "virtual customer service" feature where you scan the QR code to chat with an agent. As long as they connect your to an agent physically working at THAT airport, they should be able to also add your companion to the upgrade list.

The GS desk (or any reservations line for that mater) wont be able to add. You'll be told that the flight is "controlled by the gate" within 24hr of dep.