A lot of the outlets in my house are non-polarized two-prong types. I'd like to replace them with polarized grounded outlets. I'd rather not just install a GFI outlet, as that kind of limits me.

I can easily get at the cabling, and the outlets in question are run with two-conductor armored BX cable. My question is, can I just run sheathed 14/2 cable from a new outlet to the downstream junction box?

From what I understand, the armored sheathing provides a ground, but it's not supplied to the outlets. Will be above satisfy ground requirements? Or should I just run the entire circuit with new 14/2 cable back to the service (which will be a little harder).

(it's an old house, there's also a lot of knot-and-tube wiring still in place)

I would run a new circuit from the panel!