Permethrin is listed as a "restricted use" substance by the US EPA due to its high toxicity to aquatic organisms, so permethrin and permethrin-contaminated water should be properly disposed. Permethrin is quite stable, having a half life of 51–71 days in an aqueous environment exposed to light. It is also highly persistent in soil.
Sadly it doesn't define aquatic organisms. So may only apply to fish and water borne insects. It would depend on the quantity that gets into your system really.
Your best bet is to set up a lab scale plant and try it out before putting it into the main plant.