[PlantedRich]

Many of these questions relate to how we each may not speak as precisely as needed or we shift the terms just a touch.
So this is my view and may not fit others. I say a tank will "cycle" regardless of what we do, but only to a certain point and that is where we need to be a bit more specific and understand what I believe to be the early meaning of the term, "cycle".
My idea of cycle is when the waste is being converted from the early stages of decay where it is ammonia, to nitrite and finally to nitrate. Many might think of the cycle as being when it is safe to add fish! Some of the early use of the cycle was to set a tank up to receive a shipment of fish all at one time to save multiple shipping charges. So fishless cycle became common practice as a way to build a large bacteria colony to meet a sudden increase of fish load.
After getting into planted tanks, I've seen the term morph quite a bit to mean many differing levels of doing the same to make a tank ready for fish and that has led to many differing ideas of what we want and how we get there.
So the question may be as much about what each person wants and how he wants to get there.
To me the cycle is getting the tank ready for what we want to do. So a tank CAN be ready if the owner is also ready to make it work. A tank doesn't have to have much bacteria ready to convert very much waste if there is a lot of water and very little waste to be diluted to safe levels.
That explains why some may say a small tank doesn't cycle as they never see any ammonia as they are simply not able to measure the extremely low ammonia levels from a couple small fish. This is especially true if they are also doing large percentage water changes to remove/dilute much of the waste and ammonia.
So my answer is that a tank will cycle but we may not see it and it is also only cycled to the level of waste we are producing, not that it is ready to add a shipment of fish. A tank can set for months/years with a small load and be totally cycled for that load but certainly not cycled to add twenty more fish all at once!
Water changes will not change the amount of bacteria growing but that is assuming those changes are done correctly so that we are not killing the bacteria.
When I first started in the game, we did not cycle a tank, but simply scrubbed it all down with the hottest water we could stand and totally killed all the bacteria we might have grown! The price we paid for this lack of knowledge was doing a vast amount of work and seeing the fish occasionally die----for some unknown reason! The thinking was that we must have missed some disease in the tank and we should scrub better next time or use hotter water.
Knowledge is such a precious thing!

 

[PlantedRich]

I might guess that some of the confusion about small tanks not doing a cycle could just be the way we test for ammonia, nitrite and nitrate. When we have a small tank and small load of waste, it might be pretty easy to miss having ammonia and seeing it turn to nitrite and on into nitrate as our testing is not really too precise and then if we throw in having plants to further suck nutrients from the water. So those who might say they don't cycle may just be not looking far enough to find nitrate and jumping to the idea that they never had ammonia and never had nitrite, it didn't cycle. They might be hard pressed if asked about nitrate but then if there are plants, they may not see that either.
Very easy to find the wrong idea if we don't look close enough. One of the really good points of doing a fishless cycle is that we DO know there is X amount of ammonia as we add it, then when we see nitrite being processed to nitrate and add more ammonia, we can say with pretty good assurance that the cycle is complete! It may just be part of our impatient nature and trying to short cut the waiting that makes us come around to the tank doing something else.

 

[PlantedRich]

The idea of "cycle" is still one that gets lots of conversation going and it still slips up on us at times. The worst case may be when we have a tank for a long time and we've had fish in it long enough that we are certain that it has totally completed any "cycle". So thinking it all done, we order a big box of our favorite fish and fine we don't have near enough good bacteria built up to handle a load that may now be four times as large! There are tanks cycled and ready for one fish, six fish, or 20 fish but they are not all the same!