Affect your plants how?
If you mean will the treated algae spread to your other plants, then I would guess that depends on how well the bleach dip worked.
If you mean will the residual bleach hurt your plants, probably not, but it won't help your fish (if there is some residual bleach). From what I've read, I ended up using this procedure for a bleach dip, and things turned out fine:
I rinsed the dipped plant in tap water quickly, and then rinsed them in a bucket of water with a triple dose of dechlorinator, making sure at the end that there was absolutely no hint of a bleach (chlorine) smell.