My army of kobolds (Small, bunny-like rapidly-breeding carnivorous creatures) captured an army of 100,000 human soldiers. The prisoners were transported to my massive underground prisons. My kobolds are weak physically, so they thought to let the humans die of insomnia. What is the best way not to let them sleep if all the prisoners are locked in a massive prison and I also want to harvest their flesh for the kobold cubs? They have access to pre-mideaval tech.
Since your goal is to feed your armies fresh meat, I'm going to answer the question in the title, rather than the question itself.
No. Sleep deprivation is not an effective way to execute a large population.
First, in lab tests with rats, it takes multiple weeks for the animal to die.
The method used in this test is to put a rat on a platform that it only has enough room to stand on, but not enough room to lay on, suspended over water. This would not work for our captive humans, because they'll be able to support each other and sleep in shifts.
Most other methods, except for actively prodding people who appear close to sleep, suffer from the same problem: the captives will find a way to support each other and sleep in shifts... and as a parent, I can attest that when a human is tired enough, they can sleep through any amount of noise.
Prodding is not an option here, because your army needs to be close enough to the humans to put your kobolds in danger.
Second, because it takes so long, and you have such a large, confined population, disease will spread, spoiling your meat.
Additionally, a side effect of sleep deprivation is a compromised immune system, further spreading disease.
Since you want fresh meat, you want to avoid disease at all costs, lest you give food poisoning and icky human diseases to your glorious rabbit-kin armies.
My suggestion is to take this as an opportunity to train your archers, so that the captives die as quickly as possible (or at least in single cell-block sized groups), and work quickly to preserve the meat.