That prompted me to do a quick search. In Google, I typed in, "Can a faulty alternator cause engine run-on?"
One hit was http://www.painlessperformance.com/faq.php?s=General
In which they said, "Engine Run On.
An engine that still runs after turning the ignition key off is a victim of engine run on. Engine run on can be caused by several things.
Faulty alternator/regulator. GM 10SI and 12SI alternators sometimes feedback voltage into the exciter wire even when the engine is shut off. This causes voltage to feed into the ignition circuit which keeps the coil hot with voltage and causes the engine to keep running. Remedy this issue by installing a diode #276-1661 from Radio Shack, inline with the alternator exciter wire. Make sure to install the diode with the line closest to the alternator. By installing this diode you have introduced a one way gate in which voltage can only flow to the alternator and not vice-a-versa on the exciter wire."
So, in reality, according to this, I may not have needed to replace the alternator.
In my application, it was an externally regulated alternator, with simply an "Idiot Light" indicator.
As quickly as I found that site with that quote, I would be willing to bet that there are many other sites explaining that as well.
Unfortunately, back in the mid 70's when I had that problem, not that many mechanics were aware of this situation.