Simply stopped

Sorry no

You could remove the alternator from the car completely, and if there's enough in the battery to crank the engine fast enough "it will run." I've done it

In sometime around 71, my 70, which had had the battery go completely dead at one point (parked at a dealer, monkey left the hazards flashing) this battery was SULPHATED. Long story short, I moved the battery to the trunk, and THIS is where we discovered, on a trip from San Diego (Miramar) to "the desert" that the battery was OVERCHARGING

So we literally would drive for hours and hours with the voltage regulator unhooked, "running off the battery."

Now, admittedly, this was BEFORE electronic ignition and certainly EFI.