Drone pilots tend to (or should do) stay away from power lines because of the interference their magnetic field creates in the drone's internal compass. However, if that can be worked out you might be able to at least gain some flight time by getting a little boost from induction, even if you're not going to be able to recharge at the 10A-20A that drones burn staying aloft.
For this to happen frame design would need to be largely informed by the question of where you put the coils, and how much metal to put in them. My guess is there would be some serious challenges to make a drone light enough to fly and still get meaningful power from the magnetic field.
If a couple hundred drones are drawing enough energy to get a meaningful boost to flight time, does it start to become noticeable on the power grid?