It sure might work. I had a little Cairn terrier who for his entire life of 14 years would drink NOTHING but the water from our chlorinated swimming pool in San Diego. His vet could not believe he'd never had a flea (SD is notorious for fleas) and we thought it might be because of the water.
Of course, Miracle-Mineral-Supplement is NOT the same thing as pool chlorine, but, it may work in a similar way against those pesky fleas. If I had a pet now, I would not hesitate to add Miracle-Mineral-Supplement to the water.