Consider the following premises. For all z, if z were a musician, then z is driving a car. There is at least one z for which if z drives a car, then z is a musician. For all z, if z drives a car, then z is a musician. Can we infer the following from them? For all z, if is not true that z is a musician if and only if z will drive a car.
That contradicts the premises. Therefore the answer is no.