Not having read every insurance policy in existence, I can say with some certainty that every policy I have seen makes it clear that the use of a rental in violation of its contract voids any coverage. This would apply to coverage on the vehicle and to your driving as well.
Ask around about what a minor scratch on a Jag will cost. Then ask what it costs to pay off the hospital bills for someone else if you are found to be at fault. $0.50/mile will seem cheap.