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

Anyone who says it's ok to pull any battery cable off while the motor is running is full of ****.
That's a very stupid thing to do. Along with the previous mentioned bad stuff, the battery, when being charged even a small amount will produce hydrogen gas. The spark produced when pulling off a cable can ignite the hydrogen and the battery will explode like a bomb. Seen that happen first hand. It's not pretty.