Should car still run on alternator with ground terminal off battery?

Car will not run with the ground cable disconnected from the battery never. A method known to check the alt. is pull the positive cable. The best method is to Use a multi meter
to check for charging voltage from the alt. by first checking the volts at the battery with the key off and no lights or accessories on then star up and check again if the alt. and it's components are doing their job you should see around 14 volts on a charged battery while the engine is running