Depends; what's lighting up the field coils in the alternator? A generator, which probably went out of cars in the '60s, sure. But something has to power the parts that create the magnetic field in an alternator, and if the battery's dead...
On top of the fact that the coils on top of the plugs these days are more finicky about the amount of power they receive. A battery with 11.5V probably isn't going to cut it. And as you point out, the ECM may want a healthy 12V, too.
I would hedge the original statement and say you could push start a newer manual transmission car, but don't count on it. Even as far back as 1999, I had a Honda VFR motorcycle that could not be push-started until its battery had some juice in it, for the reasons stated above.
