Ideally, a rinse should have no peroxide and no ammonia.
It all depends on how well you upkeep your hair before and after any color treatment, but peroxide is a potentially damaging ingredient, and I wouldn't risk it.
I tried a Clairol color once with "low peroxide" and it still made my hair shed/break something awful. It was an Auburn color, I'm not sure if it's the same Clairol line you're referring to.
Also, if it has peroxide in it at all, I don't think it's a rinse. I think that's straight up dye...but I could be wrong. Hopefully someone who knows a bit more about permanents vs. rinses can help me out on that point.