Is it technically possible to add another shifter to an already functioning Di2 setup, allowing for an extra shifter at the end of an aero extension bar, hooked up to the same junction box as the original shifters, to allow the rider to shift in three different riding positions (normal, drop, aero)?
Yes, of course, that's possible. You just plug the cables into the brifters. Peel the grip-covers forward and you'll see unused ports underneath. Those may be used for sprinter buttons or for climber buttons as well.
But I'd suggest you replace a triple box by a quintuple box (Shimano SM-EW90-B 5 Port Di2 Junction A) to make the connection easier without undoing and replacing the bartape. Another advantage of the quintuple box is the fact that you can remove the aero extensions without fuss.