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

Thanks all. Thought the cable pulling damage was in reference to newer efi cars. Anyways. Will get a voltmeter on it. Alternator isnt super expensive. Just didnt want to have to replace it if it was working. Figured one of tje above tests was a quick and dirty way out as my time is limited, and I am usually working, racing, or working on the race car, opposed to this old cruiser