The battery is only needed to start the car... After the engine is running, the alternator provides all the power to run the engine and replace the charge in the battery that was used to start it...
So if the charging system is working and you disconnect the negative cable, the engine will stay running... If the alternator is not putting out enough power, the car will die...
If the alternator does not put out enough power, it will suck it out of the battery until the battery dies...
