Alternator question

1987 fullsize Bronco. I am having a problem with the battery draining when the vehicle in not in use. I am trying to troubleshoot the problem. The question I have is when the engine is running and the alternator is generating +/- 14 volts shouldn't I be able to disconnect the battery and the engine should still run? I Know I have done it in the past and the engine still runs.
So far I have pulled all the fuses and still can't find the drain.
Problem solved, it was the alternator. I load tested it and failed,but with no load it was producing 14 volts. Apparently there was a constant drain from the alternator (or regulator). I switched out the alternator and all is well.

If the diodes in the alternator are bad it will drain the battery when shut off. Usually, but not always, the battery light will go on when you shut down the engine. This indicates the alternator is draining the battery.