I always pour my bleach through the skimmer and it doesn't hurt a thing. And, so does Al (Poconos). Of course, only when the pump is running. It is diluted so fast with such a large volume of water and is dispursed so quickly that it is not a problem.

Now -- I probably wouldn't pour the bleach over a sock full of cya but otherwise, it isn't a problem. We have both done it for years.