Yes studies have shown that with regular use of depilatory creams they do reduce hair growth.
When you regularly and constantly use the depilatory creams to remove hair the hair still grows back but it tends to start to grow slowly so the hair doesn't come back as fast.
When you use depilatory creams the creams remove the hair at the skins surface by dissolving the hairs which makes it grow back smoother than if you were to shave the hair.
That also means less itching of the skin when the hair is removed with depilatory creams than it would with use of a shaver.
If you shave the hair is just cut off at the surface which can make the skin itchy.