No. Those probes actually detect an electric field, not a magnetic one. The voltage on the wire is still AC, and it will still generate a faint electric field, even if no current flows. I have had one, and they work well. The only problem is that the probe needs to be less than an inch away to detect anything. It is pretty useless for detecting the electrified puddle or tree, unless you are paranoid and use this thing on every object before you touch it.
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Darwin was wrong -- I'm still alive