Yes, when chlorine gets used/consumed it becomes chloride salt. When you add chlorinating liquid or bleach you are also adding sodium. So over time the pool builds up sodium chloride salt. For every 10 ppm Free Chlorine (FC) added by chlorinating liquid or bleach, it also increases salt by 17 ppm, unless there is water dilution. Though stabilized chlorine adds half the amount of salt (which comes from the chlorine), it also adds CYA and that causes problems far sooner than salt. Cal-Hypo adds salt in between these two, but builds up Calcium Hardness (CH).
Even after a fresh refill, if one has a plaster pool and had no salt or calcium in their fill water (which isn't usual, but let's take this worst-case example), then one starts out with around 350 ppm salt (measuring the chloride from the added calcium chloride).