* Low Voltage: A low battery produces low voltage throughout the electrical system. The car's computer (PCM) relies on a stable voltage to function correctly. If the voltage drops too low, it can cause the PCM to malfunction and throw a diagnostic trouble code (DTC), resulting in the check engine light illuminating. This wouldn't be a *problem* with the engine itself, but a consequence of the low voltage affecting the computer's ability to monitor properly.
* Sensor Malfunctions: Many engine sensors require a sufficient voltage to operate correctly. A low battery can cause these sensors to provide faulty readings, which the PCM interprets as a problem, again triggering the check engine light.
Therefore, a very low battery is more likely to cause the check engine light to come on *as a symptom* of a larger problem (the low battery) rather than being the direct cause of a mechanical engine issue. If your check engine light is on along with a low battery warning, address the battery issue first. Then, have the car scanned for diagnostic trouble codes to determine the root cause of the check engine light. It might be unrelated to the battery once the voltage is restored.