That's not learning, though. That's just taking new information and stacking it on top of the trained model. And that new information consumes space in the context window. So sure, it can "learn" a limited number of things, but once you wipe context, that new information is gone. You can keep loading that "memory" back in, but before too long you'll have too little context left to do anything useful.
That kind of capability is not going to lead to AGI, not even close.