I do that, but without the first wash to rinse the washer. Use less water and I've never seen any bad effects (and I have anemones, clams, SPS, LPS, pretty much anything that would be sensitive to soap). I'm sure two loads is plenty to get rid of any residual soap. And the remaining bleach evaporates on it's own when you air dry them.
But flipping them inside out and hosing them off works too. My dad does that and soaks them in a bucket of bleach, then hoses them off again and lets them air dry. That works fine and would be better (saving water wise) if you only have a couple of socks. When your like me and have 14+ socks, the washer is the way to go.