It's already grounded via the BX cable

Not all armoured cable is rated to act as the ground. Maybe someone more knowledgeable will jump in, but I believe the older style (BX?) wasn't but the newer stuff might be (AC?).

and the internal ground connection from the receptacle

What do you mean by this? Do you mean you have 'self grounding' receptacles? If so, then that's probably fine. But I don't think that your typical receptacle is self grounding. Are you sure that's what you have?

If you have a ground wire, I'd just connect it to the box and the receptacle whether it's absolutely required or not.

Greg is correct. Armored cable is not universal. If there is a green wire I can pretty much guarantee this isn't "BX" though people tend to use term BX for any of the ribbed armor cables.

As Greg points out, unless the receptacle is specifically rated for such, the yoke itself isn't a legal grounding means. When running armored calbe to a box you must use an appropriate fitting listed for the type of cable. Type NM clamps are not appropriate.

Type AC cable can use the armor as an equipment ground. However, my guess is you have interlocked sheath type MC cable, the latter may not be used as an equipment ground. On any modern cabling, the type should be marked on it. Old style BX can't use the armor as a ground either.