It's actually an inverse first power law, assuming that the distance of the drone from the wire is much less than the length of the wire. The inverse square law applies only to a point source of electrical energy, to a sphere, or to an object whose largest dimension is much less than the distance to the drone.
Yes, feels like perching via some insulated "feet" and only using energy for stabilisation (as opposed to flight) would allow the drone to get very cloe (and suck much more power) from the line.
It'll definitely charge faster, if only because it's drawing less power to stay up and getting closer. The only question is, is it like 10% or 100% faster?