That is suggested in the literature. However if chickens are given feed derived from grains produced in the "goiter belt", there is no reason to expect that iodine levels will be adequate. If humans are iodine deficient on local crops, then animals could be too.
So this is a trusted source of information? https://ods.od.nih.gov/factsheets/Iodine-HealthProfessional/
In the USA, iodine is now not used universally as a teat wash in dairy barns which used to get into the milk and iodine is not longer used as a dough conditioner in bread production. BTW, iodine is now a controlled substance [licensing, accounting and traceability] because it can be used as a catalyst in some clandestine drug lab processes. So that may be a factor driving up the cost of iodine.
Remember that a large portion of human populations used to be severely iodine deficient eating local crops, eggs, meat and grains/milk produced on the same iodine deficient soils.