Earlier on, when Jane Fairfax arrived, Emma thought that "she could never get acquainted with her; she did not know how it was, but there was such coldness and reserve; such apparent indifference whether she pleased or not; and then, her aunt was such an eternal talker! and she was made such a fuss with by everybody! and it had been always imagined that they were to be intimate; because their ages were the same, everybody had supposed they must be so fond of each other." (20)

Your last quote is in direct contrast to this, and I think it's a sign that Emma can take a hint (i.e. that she ought to be kinder to Jane) and also that she does not always stubbornly hang on to ideas and notions that she has entertained before. She is capable of seeing the error of her ways. So yes, I agree with you that self-improvement could be on its way for Emma (though she still has some way to go):D