The MC jacket would have to be listed as an effective ground return path. See 517.13(A). Most MC would not qualify, you would need to use type AC (BX).
years ago we used a hospital grade MC cable. in additon to the full size ground, there was a shorting lead allong the outer casing of the cable. if installed with properly rated fittings it was allowed to be used in patent care areas.
i always thought of BX as being MC cable without a full size ground, but with the shorting lead.
In nonpatient care areas MC can be used for Normal or Equipment Branches, but not for Critcal or Life Safety Branches unless you meet one of the stipulations of the 2005 NEC 517.30(C)(3).
In patient care areas, you would need HCFC, which is an AC with an insulated equipment grounding conductor, but once again you must look at 517.30(C)(3)
Earlier code cycles pretty much disallowed flexible wiring methods for the Emergency system.