Answer:

Yes, technically bleach can be used. However, the concentration of chlorine is much lower than other forms of chlorine including the liquid chlorine that you can purchase specifically for pool use. Therefore, using bleach might be advised in a pinch, but you will not save any money because the concentration is so much lower that you get much less out of the bleach than you would other forms of chlorine. There may also be other byproducts (scents, lotions, etc.) that you do not want in your pool if you can help it.