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

So I had always heard a simple alternator test is to pull the ground cable off the battery post, and see if it still runs. Had also heard you should be able to feel a magnetic pull on the back of the alternator when its working. My alternator does neither. engine Dies with the ground off the battery, and I can feel no magnetic pull on the back. Drove it to autozone and they tested the alternator and claim its good. I have my doubts....this car has killed 2 batteries since I got it. I believe it has a slow draw on the battery when off...but also not sure the original 1978 alternator or voltage regulator is working. I looked at the voltage gage the autozone guy had, and it showed over 12 even with a load.
If it matters amp meter in car shows positive even at idle.

My race car kill switch will kill the car through the positive battery cable, so the positive cable killing the car makes sense. but again I thought the negative cable could be used to test the alternator? Anyways...let me know what you guys think. Thanks.