The cockpit voice recorder and the flight data recorder operate on ESS AC power. The flight data acquisition unit operates on ESS DC power.
With all engines off and no APU, the only source of power is battery to EMERG DC/AC.
The recorders would not be operating on battery power, and would not record the information from the point power was lost (flameout).
Satcom Guru: LMI2933 LAMIA AVRO RJ85 Medellín Deadstick