You ask if there would be an electrical current if one of the plates were made of rock.
The short answer is no. Unless the rock is a very rich metal ore, rock will not conduct electricity well enough to allow a current.
When we put our hands on the metal plates, we complete a circuit, electricity flows from one plate to the other through our arms and body, and then back to the original plate through the micro-ammeter via wires. The current, which is very small, is caused by the different way the metal plates react to the moisture in our skin; one collects electrons and the other gives them up. Any two different conductors will serve the purpose. Ours are copper and aluminum; but they need to be conductors in order to complete the electrical circuit. The human body is a pretty good conductor.
Most rocks are insulators and can't complete the circuit.
