While I'm loathe to disagree with Bart (he's typically right), I have to disagree here (to a point). If you're putting in an AAW wiring harness, I can't imagine putting the 1G alternator back in. While a 1G may theoretically be adequate, in reality...the point of the AAW harness is to allow for electrical expansion and enhancement as well as wiring simplicity. If you plan on doing anything, a 3G or GM style one-wire (blech) style alternator is pretty much required. In original configuration, the original electrical system was barely adequate, and your headlights would dim and brighten with RPM changes. If all your lights are on, and you have any sort of radio, the system will struggle.
If you were going concours, a 1G would be appropriate. But you're not, as indicated by the Update kit. A 1G conversion box is just a bandaid to fixing the real problem...which is that the 1G was barely adequate 50 years ago. With the AAW harness, you've pretty much lost your (dangerous) ammeter anyway. The alternator won't change that. And while I agree with Woodchuck 100% in theory...in reality, I can't imagine going through the trouble of an AAW harness and not converting to a 3G unit. We can debate the 3G vs GM 1-wire all day, but with your harness in mind...I would say 1G is a mistake.