Yes, this is correct. As a practical matter, a KH kit will give a number to the amount of "buffer" the water has, allowing it to withstand pH change. Below about KH=4 it can be expected that the pH may make a quick drop at any time, stopping the cycle.
As a technical matter, KH is supposed to refer to Carbonate Hardness and should only be measuring the carbonates (HCO3-) (also known as Temporary Hardness because it can be boiled out) but it turns out that our kits actually measure Total Alkalinity, which is a good surrogate for carbonate hardness in our situations and so some of the general hardness aspects (Ca and Mg for instance) may indeed be a bit involved, but technically those should be mostly involved in GH (general hardness) measurements.
None of this matters to you as long as you make large water changes when the cycle is in danger of crashing or has just crashed.
~~waterdrop~~