No. The insurance plan does not cover roadside help related to driver error, such as the battery dying because lights or electric machinery have been left running needlessly, or running out of petrol.
In any case – according to the car rental agreement, you should not take the car and repair it by your self. If the car is faulty they should replace it – if you can drive the car to their service center, than you should drive it to one of their centers and they will fix the car or replace it. If the car cannot be driven, they should send someone to tow the car and give you a replacement vehicle.
The insurance does cover damage resulting from an accident or vehicle theft, as well as damage usually excluded by rental companies, such as single-vehicle accidents and damage to the tyres, windscreen, undercarriage, and roof.
Please see the Product Disclosure Statement (PDS) for the complete terms and conditions.