In hydroponic pepper production we experience high levels of Chlorate in the fruit, while the concentration in the water is low and we don't use any KCl fertilizer.
Hopefully you might be adding other fertilizers which contain Cl like CaCl2, NH4Cl or MgCl2. Kindly check for the composition of multi nutrient water soluble fertilizers .
I suspect you mean chloride not chlorate. If chloride then yes it's taken up from either the hydroponic medium via the roots or from foliar application of nutrients. The common source is KCl.
There are good tabulations of data about chloride toxicity in plants, which is diagnosed by analysis of the youngest fully expanded leaf. Excess chloride should cause burning of the leaf margins.
Is any 'chloride' source (except you said no KCl added) in your hydroponic solution? In the attached article, it says that 'chloride' is VERY EASY to be absorbed by plants.