I have in fact delivered pizzas as a W2 employee, and had to use my own car. While I didn't ask if they'd provide a car for me, because I've never heard of such an arrangement, I highly doubt the answer would've been yes.
I've done the same job. They pay the employee per mile, an amount that is intended to cover fuel and maintenance for a typical car. The rate they pay is presented to you before you accept the position at the company and if it is not agreeable to you then you don't have to take the job.