Yes, that is what the medicated feed is for. Sulmet and Corid are the only two treatments I know of. Corid is amprolium, the same thing that is is most medicated feed. It blocks thiamine uptake in the cocci, slowing their growth til the chicken can build a natural immunity. Sulmet is an antibiotic, and is rougher on them than Corid is. There are different strains of cocci. I don't think Sulmet will treat all strains of cocci. Of course, a vet making these determinations would be the ideal way to go, though not feasible for many of us.
Cocci are in the soil so the chick would have had to be exposed to the soil or to other chickens who have been on the soil. Some areas have much heavier concentrations in the soil than others.
It is possible your county extension agent would have some information on chicken diseases in your area that you would find helpful.