Whilst washing birds will drown the majority of lice , depending on how many birds you have , it could be very time consuming and not even the nastiest potions will kill the eggs.
I would believe that Fancy. Having washed my kids hair in the most horrendous smelling chemical concoction from the chemist (did you know those lice shampoos are carcinogenic even) only to watch the lice crawling around quite happily when I finished I would doubt a chicken lice infestation could be totally cured that way either.