I got a ruling here that the answer would be yes, no.
I was doing "draw" inspections for an engineering company and I questioned the redundant ground. It was escalated and they came back that a dentist chair was a patient care location.
I suppose your mileage may vary so I would ask the AHJ where you are installing this.
You still need a metallic wiring method for the first ground.
517.13 Grounding of Receptacles and Fixed Electrical Equipment in Patient Care Areas.
Wiring in patient care areas shall comply with 517.13(A) and (B).
(A) Wiring Methods. All branch circuits serving patient care areas shall be provided with an effective ground-fault current path by installation in a metal raceway system, or a cable having a metallic armor or sheath assembly. The metal raceway system, or metallic cable armor, or sheath assembly shall itself qualify as an equipment grounding conductor in accordance with 250.118.
In my case it was ruled that MC cable is not a redundant ground. "Medical" AC (with the green wire) is. Otherwise you are in metal pipe.