I see what you're saying but the analogy has some problems. The first is that the mass of the food in the water is enormous compared to the bacteria. I'm working on getting a piece of data I'm missing, the mass of an average cell, but suffice it to say that even 0.10 ppm of ammonia in an average aquarium is a tremendous amount of available food for a bacteria. Second, my analogy prompts images of a conveyor delivering discrete packets of food at regular intervals so that there is a chance if you remove all the food from the table (a 100% water change) you get the idea that someone might reach for a piece of food and find none before the conveyor brings something else to eat. This isn't the case. Ammonia production in the aquarium is for most part a continuous function. It's more like a conveyor spilling a stream of rice onto a table or a hose spraying water than a conveyor bringing steaks.
1) I reiterate, if the bacteria can consume the excess ammonia in the water then you have a cycled tank. Excess ammonia in the water represents a tremendous excess of food. Most of us are familiar with the cycling graph. Here's the thing, the point where the amount of ammonia in the tank ceases to increase is the moment you have sufficient bacteria present to deal with the ammonia production of the inhabitants of the tank*. Same with nitrite. When the amount stops increasing you have enough to support your tank's inhabitant. The rate the bacteria are consuming the food in the tank is equal to the rate its being created at. Any bacterial growth beyond that represents overpopulation to deal with the excess.
2) Bacteria are consuming pollutants in the tank as quickly as they can at all times. Bacteria aren't like humans, they won't stop eating because they're getting fat or because they're full. They eat everything they possibly can and reproduce as fast as they can. Therefore excess nitrogenous substances in the water represent food that absolutely can not be consumed at the moment by the current bacteria. The bacteria consume the amount of food they can, it doesn't matter how much is present beyond that amount, it makes no difference to the bacteria.
3) The mass of ammonia in a 50 gallon tank with 0.10 ppm ammonia is approximately 30,000,000,000 (30 billion) times more massive than a single bacteria. There are of course far more than just one bacteria in your fish tank but even if you have 3 trillion bacteria in your tank each individual bacteria has 1% of its body mass of excess food available on top of the continual production that is part of the tank. To give some perspective that's like your average man having a hefty steak dinner with all the trimmings on the table in front of him to work on while even more is being brought. Simply put, even at 0.10ppm ammonia (which my API test kit won't even measure accurately and represents a 60% water change when your ammonia is at 0.25ppm) there is still a lot of food for the bacteria in the tank.
Based off what I know and what I've seen it is my opinion that water changes during cycling have no negative impact on the length of the cycling process.
*Obviously this mostly has to do with fish in cycling which is a far more precise process than fishless cycling. Fishless cycling is easier on fish but not very precise in terms of the size of your bacterial colony at the end. That's why it is CRITICAL that if you fishlessly cycle you take the addition of stock slowly and carefully. You CAN NOT fully stock an aquarium immediately after finishing a fishless cycle.
**My math in this is based of an approximation of the mass of a cell, 0.6 picograms. I was unable to locate the mass of a nitrifying bacteria so I took used the mass of an average sized bacteria.