Let's file this under "a whole lotta stuff goes on while the tank is Cycling"
White cloudy water can happen during the cycling process, and frequently at other times, but it is really not part of the Ammonia --> Nitrite --> Nitrate bacteria colonies we wait patiently to form and refer to as the nitrogen cycle.
White water is usually a bloom of protozoa and/or bacteria which flourish after the water is detoxed. They are the beginnings of the OTHER bacteria colonies which inhabit the tank. The bacteria that breaks down organic waste, fish food, detritus, rotting plants etc. These bacteria can produce urea (an ammonia compound), which can on occasion overwhelm the nitrifying colonies (chronic overfeeding is a good example).
A lot of so called cycle boosting additives contain these bacteria and not the nitrifying cycle completing bacteria. They are helpful in the tank but have nothing to do with the nitrogen cycle as we refer to it.
White cloudy water is rarely harmful, just annoying.
FYI: white water can also be caused by tiny almost microscopic bits of dust and debris (called fines) from the gravel or sand. The light reflects off of them giving a cloudy appearance. Sometimes there is a combination of both bacteria and fines.
Both are very difficult to filter out without specialized equipment, but will settle out or leave the water column on their own.
Jay