You would want to verify that any vehicle you drive is insured and not rely upon SR-22 insurance to provide the necessary vehicle coverage. The owner of that vehicle is required to insure it. Your non-owners SR22 policy would be secondary to that insurance. A non-owners SR-22 policy typically doesn't contained coverage for the vehicle (Physical Damage) or other necessary coverages like PIP, UM, and/or PD. (Have more questions about SR-22 and car insurance? See "SR-22: The questions drivers ask most.")
If you borrow a car from a friend and get into an accident in a that car, your friend's insurance would kick in first. But if, for example, the accident was your fault and the damage to the other driver's property exceeded the liability limits on your friend's policy, your nonowners insurance policy would cover the excess (up to policy limits).
Comment Update: If the vehicle's insurance policy lapsed or was not in effect, the non-owners policy would cover the policy holder if they are in an accident, but be aware that a non-owners policy covers liability only, not the vehicle.
Comment Update: Typically, in most states SR-22 insurance would NOT provide proof of insurance for an uninsured vehicle. Proof of insurance must conform to the minimum requirements in a state and the coverages contained in a non-owners SR-22 policy are typically just liability coverage.