In old BX cable, can the shieth be used as a grounding electrode?
Its an interesting question, updating old wiring methods and boxes for modern equipment grounding.
The 1959 NEC was the first edition that required BX to have the internal bonding strip and added a section that allowed BX (type AC) to be used for equipment grounding.
If you encounter old BX
without the little internal bonding strip and your installation
conforms to the code in effect at the time, you would need to consult the old code say for example the 1956 NEC.
Going by the 1956 NEC to use the cable sheath as an equipment ground you would have to use table 2595 as required by section 2611, which would require at least a 1/2 trade size cable armor.
That would be pretty big stuff probably not seen in residential, but perhaps a range or dryer.
That's just my take, I was not around back then.
But I have demo'ed lots of wiring from that time. If you have noticed how the first things required to have and equipment ground were wired ( laundry receptacles and bathrooms ) the installers of the era often ran a #14 often attached to the back of the boxes to a local water pipe in the room.
So if they had today's requirement for equipment grounding and pre 1959 BX I imagine they would have used 3 wire cable or ran a separate ECG.