No...it won't do any good
Anything added to the tank just exhausts itself very quickly--usually within 24 hours. The LAST thing you want to do is add a little bleach to each fill, 'cuz bleach is corrosive. Contrary to popular belief, algae growth in the tank is not a problem because algae cannot grow without light. So most foul water doesn't originate in the tank, but in the plumbing--molds, fungi and bacteria that thrive in DAMP dark places. The best thing you can do is USE your water...or at least drain and refill often. And recommission the system annually or when the water starts to taste and smell funky. Directions are in my book...or, you can hunt 'em down in the archives.
