Assuming flight conditions are good, there would be a region around the wire (line of charge) with an electric/magnetic field that the drones could use, any shielding notwithstanding.
Drones consume a lot of power while in flight. You can get a little bit of power out of powerlines standing underneath them with some tricks, but it's not enough to keep a drone in flight. At least not without something prohibitively large to couple to the line.
It's also risky to hover near a stationary object because the longer you hover, the more you're exposed to the risk of a wind gust knocking you into the nearby obstacle.
to power a running drone at more than a few inches would be just...a lot.
You get a million times more power if you can put a coil 1mm away from the wire than if you hover 1 meter away.