I flew the 777 for seven years and no-the transponder would be load shed if they were down to the Ram Air Turbine. However, if their were an electrical fire in the electronics and equipment bay it would take out the transponder, the comm radios and eventually the artificial feel unit used to produce feedback in the controls.The "Gimli Glider" possibility crossed my mind.
They ran out of fuel on a 767 and made a sucessful landing on an old airfield/drag strip.
The emergency generator prop deployed for them, if it failed to deploy you would have
an unpowered glide for 30+ miles and a ditch. May lose hydraulics.
Scott Essex, does the transponder stay live if no power exist?
Is it battery attached/essential?
The other option seems man made with the transponder off.