Can the alternator run the car by itself?

[P.S.]

Several weeks ago, was on a nice 40 mile trip in the A when it was getting close to sunset. Had just pulled a real long hill and pulled over at the next opening to let traffic go by. After 6 or 7 cars went by, nobody coming, pulled out and was going again. Turned on the lights and was driving merrily away for a few minutes, then suddenly, the car just lost all it's "go" and went BANG!. Luckily, there was a wide spot to pull over (not many on this narrow, 2-lane winding road), so pulled off. Troubleshooting revealed that the 30 amp fuse installed on the typical starter-mount bracket was open. Installed a new fuse, and made it the rest of the way without incident.

Troubleshooting for a couple days afterwards revealed no wiring trouble or anything amiss. Besides having a 6 volt pos gnd alternator, the car has full halogens front and back. The lights draw around 22 amps total, then add the ignition system current draw, and you're getting even closer to that fuse's breaking point. The fuse was several years old, decided it just gave up out of age and stress.

Anyway, that isn't the purpose of this post. Here is the actual question-

When the fuse blew, the car was running at 45-50 MPH and the alternator was putting out enough amperage that the ammeter was still showing "charge". So, when the fuse blew, the only thing it did was disconnect the battery from the electrical system. The alternator was still putting out enough that it should have kept the car running, correct? Or, do these automotive alternators stop putting out current if they detect no battery?

I really don't know much about cars, I'm an electrical guy. So to me, this is really confusing. Can any of you car guys shed some light on this please?? Shouldn't the alternator be able to run the car without a battery?