Any self exciting one wire unit I'm familiar with will make enough juice to keep everything up and running after the battery is taken out of the system - once it is energized and charging. The stuff I'm familiar with need to see a certain RPM to energize and will continue to provide current after that.

Depending on the alternator, he may be telling you the truth and not know it's incorrect - if he hasn't checked it properly. If it's making voltage, it will keep the system up. Years ago, when use of alternators became popular, NHRA tech would make us start the engine and turn the master off to to see that it shut everything down. Mine wasn't wired correctly and I was careful to not let the engine rev over 3000 to keep the alternator from energizing. Then they wised up and would make you rev the engine above 3K and shove the switch off. Had to redo mine at that point.