Here is some info that answers your question:
Excerpt:
Many people traditionally believed that shaving would cause the hair shaved to become thicker and darker. However, this bit of conventional wisdom has been disproven. The resulting stubble only makes the hairs seem to be thicker, as a shaved hair has a blunt end as opposed to the tapered end of an unshaven hair, and because hair is often darker in color near the root. Clinical studies have demonstrated that shaving does not have an effect on hair growth rates or density (see medical data below).
http://en.wikipedia.org/wiki/Shaving
BTW
I believed that it did work by making each hair thicker until I just read the above article.
As a matter of fact my father attributed his sandpaper-like facial hair to shaving at too early an age. So even though I am now confronted with this new view, I am not 100% sure that it doesn't work. So you might just want to ignore the info and try it and see for yourself.