BCAA provides you, not your vehicle, with 24 hour Emergency Road Service anywhere in Canada or the United States no matter whose car your travelling in (including a rental vehicle). However, it does not provide vehicle insurance coverage.
You would be able to purchase vehicle insurance coverage through the car rental company; ICBC has a coverage for vehicle rental insurance for $10.00 per day, and if you qualify you may purchase RoadStar through ICBC for $21.00 per year (The RoadStar Package's Rental Vehicle Coverage protects you when you are driving a rental vehicle or courtesy car) only in North America excluding Mexico.
For more information on the RoadStar click here .