Can you ground to conduit?
Thereof, can you run a bare ground wire in conduit?
Running bare ground wire in a metal conduit is a waste of time, as the inevitable contact will render the two ground systems homogeneous. If you are pulling wire through conduits, you should be pulling single strand individual insulated conductors.
Besides, can EMT be used as an equipment grounding conductor?
In addition to system grounding, electrical systems require equipment grounding and bonding to safeguard personnel. Rigid metal conduit (RMC), intermediate metal conduit (IMC) and electrical metallic tubing (EMT) are permitted per 250.118(2), (3) and (4) respectively as an Equipment Grounding Conductor.
The appliance will operate normally without the ground wire because it is not a part of the conducting path which supplies electricity to the appliance. If the case is grounded, a high current should flow in the appliance ground wire and trip the breaker.