It Shouldn't I would not think so! Have Fun!

If anything it will probably make you lose the vibrancy of the hair color. You have to remember that there is chlorine in the water and sometimes hints of bleach. So you want to be sure to have a really good conditioner for afterwards too.
There is a difference though BLEACING/HIGHLIGHTING is a completely different element. If you highlighted or bleached your hair...YES the chlorine might turn it green. If you have dyed your hair red, the chlorine can turn it a shade of orange( it happened to me) if its just brown/black....chlorine normally won't affect the color but it will dry it out and that's why I said get conditioner!

No, it shouldn't. Just might fade/dry out your color.