You can still eat the eggs from birds who have had bluekote applied.
That said, I'm not crazy about bluekote. I used it once on some hens I had rescued from an eggfarm, and it really did nothing but turn the chickens an awful shade of purple. This purple will last on the feathers almost indefinitely, until they molt.
Instead, I would try to look at other ways to address the picking. I would try
1. chicken saddles that would cover their backs and protect those back feathers. You can make chicken saddles (use the search function on this forum to find out more), or buy them. There are at least two websites you can buy them from, and a member here named Moodene (sp?) was selling them for a good price, she might still be selling them
2. Make sure they have enough space inside the coop and in their run (if they have one).
3. Make sure they are getting enough protein. Sometimes picking is caused by a lack of protein in the diet. Feathers are high in protein.
4. I would keep them otherwise occupied by bringing them nutritious treats at least once a day to peck at and get excited over. A bored chicken is a misbehaving chicken.
