non chlorine bleach question

Of course non-chlorine bleach works. Bleaching products (as well as UV rays from the sun) will weaken fabric to some degree. It all depends on the concentration of the bleaching product, temperature and duration. I probably would not soak fabrics in any bleaching product. You can use chlorine bleach with white cotton fabrics, but again, the wash should be agitating when adding bleach. Sometimes just a 1/4 cup of bleach will brighten whites with a lower risk of fabric damage and at a fraction of the cost of non-chlorine products. Mom said, "To keep whites white, wash whites with whites and only whites!"