Perhaps, pretty simple to do the math though. Lets plug in some numbers and see what is what.
First we'll assume that the weight changes altitude by 2 meters, next we'll assume the "weight" is 5 kG (about 10 lbs) it could be more than that if you used denser material but it looks like they are expecting you to fill a sandbag to weight it dry sand is about 1600 kg/m^3 [1] so a sandbag that was 15cm/side would be about .0033 m^3 or 5.3 kg.
The force exerted by that sandbag, 2 meters up is 5 * 2 * 9.8 or 98 Newton-Meters. Now the campaign says it runs the light for 30 minutes so to find the power in watts we take 98 Newton-Meters divide by 1800 seconds (bag goes from 2m to 0m in 30 minutes) and get .0544 watts per second. Assuming the generator is 50% efficient (that is a really good generator) that is about .025 Watts to run your LED. So can you get decent light from an LED with 25 mWatts? At a forward voltage drop of 4V (White LED) that is 6.2 mA of current. (updated to be a decimal order of magnitude smaller)
Given that current LEDs are seeing something like 50 lumens/watt you might see 2 - 5 lumens from such a light. Not nearly as bright as I originally estimated.
from the caption under the house door/garage images:
Hang it in the shed or make it into a great porch light, you can clip on a hanging basket or anything weighing about 20lbs.
So that's ~2x your estimate, which doesn't seem impossible.
I do wonder what they're suggesting using for the ballast though, that avoids excessive bulk. Another consideration is going to be finding a suitable mounting point in a typical shack/slum type dwelling.
First we'll assume that the weight changes altitude by 2 meters, next we'll assume the "weight" is 5 kG (about 10 lbs) it could be more than that if you used denser material but it looks like they are expecting you to fill a sandbag to weight it dry sand is about 1600 kg/m^3 [1] so a sandbag that was 15cm/side would be about .0033 m^3 or 5.3 kg.
The force exerted by that sandbag, 2 meters up is 5 * 2 * 9.8 or 98 Newton-Meters. Now the campaign says it runs the light for 30 minutes so to find the power in watts we take 98 Newton-Meters divide by 1800 seconds (bag goes from 2m to 0m in 30 minutes) and get .0544 watts per second. Assuming the generator is 50% efficient (that is a really good generator) that is about .025 Watts to run your LED. So can you get decent light from an LED with 25 mWatts? At a forward voltage drop of 4V (White LED) that is 6.2 mA of current. (updated to be a decimal order of magnitude smaller)
Given that current LEDs are seeing something like 50 lumens/watt you might see 2 - 5 lumens from such a light. Not nearly as bright as I originally estimated.
EDIT: The time was wrong 1800 not 180
[1] http://www.simetric.co.uk/si_materials.htm