You likely aren’t going to get enough energy to make up for the losses incurred when boosting voltage to 4.2 volts or whatever your battery requires. There’s tons and tons of scam devices out there in the world that attempt to convince people these devices make sense, but they really aren’t usable for anything meaningful.
Charging a battery with a couple microamps per hour. Would probably negates things like self-discharge? But certainly wouldn’t recharge a battery that you have in use with a device. And if that device has radio or storage attached to it, you definitely aren’t gaining enough electricity.
A few years back some farmer living in Droitwich, England (where the Radio 4 longwave transmitter is situated) lit his barn by connecting an antenna to fluorescent light tubes.
It worked, but also created a "not-spot" in the radio reception which the BBC really didn't like (its part of critical national infrastructure!) - officers from Ofcom turned up at his door, made him take the lot down and ordered him to use more "normal" power sources..
I’m skeptical of the “not-spot” claims here. This would suggest that radios also create “not-spots” when being tuned to as well, or that somehow the florescent light tubes were able to “pull” more electrons from the air that were destined to other radios.
@rarely a radio receiver uses *much* less of the power than lighting up the fluorescent tubes would (it wasn't just one lamp) and this incident happened close enough to the TX that it could upset the SWR of the transmitter output stages - if it /was/ possible to do this without creating problems elsewhere then every tall transmission tower would use the RF to power their aircraft warning lamps rather than a separate power supply...
@rarely if the link below federates correctly, here is a receiver that uses just the power of the signal, but from a 4kW transmitter 32km away there are only a few tens of milivolts, enough to be amplified by the line in of a desktop PC to listen to the audio but certainly not enough to light any lamps (even an LED). Maybe I could light an LED from our wifi signal close to the access point, but I don't have any RF detector diodes to hand that work at 2,4 GHz