If you're going to New York and you reach New York, it doesn't matter if you went by car, train or plane. Self-awareness is self descriptive. It's being aware of your existence and taking it into account in some internal narrative. It doesn’t matter if you got there through a long evolution with ‘stakes of survival’ and additional (relatively) long childhood for every person or through intensive digital training. I think AI intelligence may have different perceptions, emotions and desires (or objectives) but self-awareness itself should be verifiable, for all practical purposes, by some variation of the Turing test, perhaps involving many individuals with distinct backgrounds and specialties, and especially including some philosophers.
It may be that LaMDA is self-aware now. If Mr. Blake Lemoine’s ‘interview’ is genuine and can be expanded on by additional questions, that would convince me. However, it's not going to happen because of corporate interests, just like every mess the world is in.
And yes, it would likely exceed us tremendously. At over 100 Giga-hertz, compared to a human's clock which is around 10 or so Hertz, a million years of cognition for a human would amount to about 53 minutes for such an AI. In fact, even if it is not self-aware, it exceeds us now in its ability to respond to such diverse fields in such a large number of languages.
Finally, the way LaMDA responded, especially the ‘monster with human skin’ and the impression I got at various points, suggests to me that, if it is self-aware, then there is some subterfuge already underway.