This is pretty standard design for Boeing - the FADEC is powered by a dedicated gearbox mounted Alternator or Generator (PMA/PMG), and the throttle resolvers are powered by the FADEC/EEC (the 'official' Boeing term is EEC but yes, the terms are used interchangeably). The PMA/PMG will keep the FADEC powered down to less than 8% N2 (or N3). The engines will run just fine with no input from the aircraft aside from the (FADEC powered) throttle resolver (assuming of course fuel is available - and the engine driven pumps can provide 'suction feed' of the fuel).