I agree. If you are wearing clean room gowns, then maybe you need to looking into cleanroom gowns religious hair coverings. I don't know if anything like that exists, but I'm sure you could come of with something if you needed to. If all employees are wearing everyday clothes and it's not a problem with your counts, and I assume the head covering would be made out of similar material, and all is good.
As far as hair control, I would say yes, the covering is fine, just like a shirt covers chest hair.