You would likely be better off with a diode bridge with very short leads across the LED, and a couple of quarter wave wires (about 5 - 6cm? for 900 MHz) attached for the input.
I'd expect multiple diodes like that to lose more voltage than they pick up? Possibly the lead lengths combined to form a resonant loop in the original - or it's just a scam video..
Mobile phones use a digital time division multiplex when active in a call, they transmit for 1/16th or 1/32 the time if I remember right.
When not in a call, they just refresh the link to the whichever cell they are connected to occasionally, so the phone system can direct an incoming call to the appropriate cell.
If you call someone (or you own land line) you should get a steady signal, though the average will be a fraction of the actual transmit power.
The GSM system also feeds back the receive signal strength from the cell to the phone, so it can modulate the TX output depending on distance and path loss, to minimise power and maximise battery life. eg. If you are close to a cell tower, the TX power will be very low & if you are near the range limit or there are obstructions, the power will be high.
This is a gadget I built last year for a similar experiment - it uses two approximate half-wave dipoles for 900 & 1800 MHz, with surface mount ultra high speed diodes tapped at a moderate impedance point on each leg, to smoothing caps and resistors to merge the output.
It gives readings on a meter, but it's extremely sensitive to both its own and the phone orientation and distance etc.
(The resistor junction is well clear of the support - it's just the angle that makes it look like it's touching).