Under the doctrine of "respondeat superior", can an employer in
Michigan be legally liable if an (intoxicated) non-salary employee
hits and kills a person on their way to work?
For most purposes, under principles originally established for minimum wage laws under the Portal to Portal Act, you are not at work and acting within the scope of your employment when you leave home to go to work (i.e. when you are commuting) or when you leave work to go home at the end of the day.
Would the employer's legal responsibility change if the vehicle was
owned by the company?
Not on a respondeat superior theory. The employee still isn't acting within the scope of employment.
But, Michigan does impose statutory liability upon vehicle owners which is vicarious liability even though it isn't respondeat superior liability, under a theory similar to (but broader than in some respects since it applies to non-family too, and narrower than in other respects since it is limited to vehicle owners) the common law family car doctrine. Specifically, Michigan Vehicle Code § 401(1) states (the balance of the section pertains to leased vehicles):
This section shall not be construed to limit the right of a person to
bring a civil action for damages for injuries to either person or
property resulting from a violation of this act by the owner or
operator of a motor vehicle or his or her agent or servant. The
owner of a motor vehicle is liable for an injury caused by the
negligent operation of the motor vehicle whether the negligence
consists of a violation of a statute of this state or the ordinary
care standard required by common law. The owner is not liable unless
the motor vehicle is being driven with his or her express or implied
consent or knowledge. It is presumed that the motor vehicle is being
driven with the knowledge and consent of the owner if it is driven at
the time of the injury by his or her spouse, father, mother, brother,
sister, son, daughter, or other immediate member of the family.
So, unless the employee had a company car without the express or implied consent or knowledge of the employer, the company is responsible for harm caused by negligence.
There might be an argument that criminal activity (driving while intoxicated) which was intentional or reckless, is beyond what the employer gave express or implied consent to do and was not done with employer knowledge (I haven't reviewed the case law to examine that theory), in the same way that the employer would probably not have liability if the employee, while sober, intentionally murdered his ex-wife by driving over her with the company car.
But, at first blush, it looks like the employer would be on the hook if it was a company car, since drunk driving is a traffic statute that was violated for which the negligence per se liability referred to in the statute would apply.
The fact pattern of the question is notable because it catches a case where there is statutory liability in Michigan, despite the fact that neither the family car doctrine, not respondeat superior, nor a negligent entrustment theory would impose liability on employer at common law.
(There are negligent entrustment cases at common law in Colorado and elsewhere where negligent entrustment liability is imposed when an employer allows a drunk employee to leave work in a company car that the employer could have forbidden the employee to use because the employee was drunk.)