Hm, let's take the energy needed to let the phone connect to the towers and make it charge the battery. At least that's my take on it.
GENIUS.
Well, actually... If this idea DID work, it wouldn't take any more energy away from the towers.
Think of it like installing a solar panel... that does increase the load on the sun and it won't make the sun dimmer... although it would block something in its path (so if this device harvested the energy from cell signals, it's reasonable to consider that it would also block them getting to the phone, as it's a case and will surround the device.)
Anyway, it won't work, because the received power is well under a milliwatt. My phone has 2/4 indicated signal strength (arbitrary units) right now and shows -98dBm signal strength (under Developer Options menu), which is about 0.1pW. During normal use, I've never seen it go beyond -70dBm.