Can you really pull a battery cable and the engine still runs?

I assume you had to start with the battery connected then disconnect it? I guess the alternator probably powers the field coil at that point. I didn't think of that. Still, pretty sure bad for alternator and electronics.
Absolutely. It can pop a diode right quick like. I've been lucky and never done that. Only reason I've ever done it at all was because I was in the field or I did not have access to a meter or charging system tester.