Yes, as long as the battery has power it can start. The car starts by relying on the starter to drive the engine, then the engine drives the generator to store electricity.
How to determine if there is a problem with the car generator:
After starting the car engine, use a voltmeter to measure the voltage on the + pole - drums. Generally, the normal range voltage will be (heating) (idle) around 12.3~14.3V, which is normal.
2. After the car engine starts, use a clamp voltmeter to clamp the generator output wire (specifically, the wire from the generator to the battery, usually marked red or blue). Generally, this is normal. The range voltage will be around 12.3~14.3V (warm-up) (idle), which is normal. If the above voltage range appears, it can be considered normal. If it exceeds, it can basicallymay be considered abnormal. If the voltage exceeds 14.3 V too much, it is considered that there is a problem with the voltage stabilizing component. the voltage drops too much beyond 12.3v. If yes?, it is considered that there is a problem with the rectifier component, the carbon brush or the rotor stator. The components mentioned above can all be replaced independently. It is recommended to start with the simplest and cheapest ones.