Yes. It won't hurt the chicks. It limits uptake of thiamine, but not enough to harm chicks in the amount that is in the food. Lack of thiamine kills off cocci. It's such a low amount of amprolium that it won't get all the cocci and that lets the chicks immune system learn to deal with it.
A lot of people get confused on what medicated means on chick feed and think it's antibiotics.
Cocci developing a resistance to amprolium is really only a concern in large flocks like commercial poultry.
Oh and adult birds can eat chick food just fine. There is no need to transition to layer until the old food is gone. Layer is only 16% protein so I don't feed it at all. My birds tend to pluck and eat feathers if their food drops below 18%. Some breeds just don't do well on the lower feed. So I feed a 20% food.
Protien also effects egg production. You can buy Nutrena Egg Producer which is 20%. Protein is expensive so it does cost $5 or more a bag than regular layer.
Oystershell or crushed eggshell is offered for the hens here. That is the extra thing added to layer feed. That much calcium is hard on the kidneys of non-laying birds like roosters and chicks. Another reason I don't feed layer because I have a mixed flock.