[gravescale]

Yes, inductively coupling to something increases the load on the primary (or any transformer would be a free energy generator). If it were using only the heat differential between the conductor and the air, like a Stirling engine, then no. In fact, if it acted to cool the powerline, it would probably increase efficiency, to a microscopic degree. And at that point, you'd get better performance from a solar panel.

However, inductively stealing a drone-portable battery on any practical time scale would be all but imperceptible on a powerline at 100kV carrying 500 amps (50MW).

If it's a UHVDC line (or any kind of DC), inductive coupling won't work at all.