The main concern I'd have with grounding the armor of BX cable is that you don't know what other metal that BX might be touching. The cable may contact ventilation ducts, plumbing pipes, even gas pipes, and so if the ground ever became energized in a failure situation, so would these other things. Exposed metal that becomes energized may also pose a fire hazard if it arcs to any flammable substance.
It is OK according to the NEC to use the sheathing of BX wire as a ground, IF the wire contains a "bond strip". This strip or wire ensures proper continuity along the length of the armor to avoid issues with an open ground. However, the bond strip itself does not have low enough impedance to be used as the ground wire by itself; you must clamp onto the armor sheathing in order to ensure a good ground connection. Many electricians recommend wrapping the bonding strip back up around the cable armor and thus clamping onto both. By "clamp" I mean securing the armor sheathing to the device box, which if metallic will provide proper continuity to receptacles and switches. If the box is nonmetallic, you must additionally connect a bare ground wire by inserting it into the clamp along with the BX, and then connecting it to the ground lug of the first device (and daisy-chaining additional lengths to other devices).