I'm not licensed electrician, but my gut tells me Yes, you do need copper ground wire between the ground lugs on junction boxes, because the conduit connections are intended only for mechanical protection of wires from physical damage, and the conduit joints and connections won't necessarily provide good low impedance ground like copper wire. So without a copper ground wire, a fault in the new switch box may not be sensed by the ground wire or breaker in the big box.
Maybe you can ground the new box via another nearby grounded fixture, box or a ground wire nut nearby. Hooking into a copper ground wire that comes from the inaccessible ground buss.
EDIT:
I was wrong...
https://www.jlconline.com/how-to/electrical/grounding-electrical-boxes_oAccording to this electrician, metal conduit is acceptable ground between boxes. Sorry!