Yes, but which wires is pretty critical, from a safety standpoint.
Your analogy to a toilet shutoff valve is not just imperfect, it’s inapplicable. The shutoff valve is upstream of the toilet, so no water will flow through any part of the toilet when it is closed.
The air gap, as @SmartHomePrimer explained (better than I could, so thanks for that), would be more like a component that locks the flapper of a toilet bowl in a closed position (AFAIK such a component doesn’t exist in real life, but it’s just an analogy). If you were to mess around with the float on the inlet valve, water could still flow into the toilet tank. If you wanted to fish something out of the bowl, then yes your hands should stay dry.
If water flows where it shouldn’t, then your biggest problem is probably the cost of repairing water damage.
If electrical current is flowing somewhere that you’re not expecting it to, you could have a potentially lethal problem.
It’s really important to understand how you could end up getting zapped if you insist on working on an energized electrical circuit.