If you are arbitarily adding more ammonia daily then yes, nitrites will appear and ammonia will also continue to register. Some people add ammonia and stop adding it when nitrites appear. What some people lose sight of is that there are two unrelated types of bacteria involved. And when ammonia is no longer being added then the type that convert it to nitrite stop reproducing and even go away. Likewise, when nitrite rises and falls it doesn't guarantee that these types of bacteria are still present in numbers to support a new tank full of fish.
I contend that fishless cycling in most cases is a waste of time, it is haphazard in most cases and leads people to the false belief that a tank will at some premeasured point be ready to be populated by fish.
There is no data that has been presented to come up with a standard forumula that guarantees a certain level of each type of bacteria. Indeed, because these bacteria are very slow growing and that the growth is variable on other factors like temperature, hardness, oxygen level, and other factors, there can be no standard formula.
Many people fishless cycle and add a tank of fish, oblivious to the fact that their tank will continue to "cycle" and have ammonia and nitrite spikes, a situation that may occur in a new tank that is cycled with fish.
Fishless cycling, unless fully understood and very carefully analyzed is a waste of time and as I said, presents a false security that a tank will be able to be stocked at the end,,,at the end which doesn't exist, because cycling never ends.
Bill