Correct. Do NOT pull battery cables on a running car
It has the potential to damage electronics, but WORSE it is NOT a good test. WHY?
Two possibilities..........
1.....Let's say you have a car with a "bunch" of loads, a great big fuel pump, electric water pump, big electric fans, and an 80-100A alternator.
Let's further say that this alternator has some bad diodes and that it's only putting out.........?? 20-40A or so.
So it's BARELY working. You sit there idling fast enough that it will "run the engine" pump and ignition, and you disconnect the cable and it keeps right on running. You WRONGLY conclude that the alternator is "OK"
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2......Situation there is actually NOTHING wrong with your alternator, but you have the engine idling a bit too slowly, and you pull the cable.......and the engine quits. You again WRONGLY conclude the alternator is bad, when if fact the engine is simply idling too slowly.
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As above check battery with voltmeter. If there is any doubt charge the battery and retest, and or test the battery. A battery going bad........dead cell, etc, can give you skewed results