Edmund did have quite a lasting influence over Mary -- in the concluding chapter it says --
"Mary had had enough of her own friends, enough of vanity, ambition, love, and disappointment in the course of the last half–year, to be in need of the true kindness of her sister’s heart, and the rational tranquillity of her ways. They lived together;" and they still lived together after Dr Grant's death i.e. Mary was still unmarried because although she had many admirers, she found it difficult to find "among the dashing representatives, or idle heir–apparents, who were at the command of her beauty, and her 20,000, any one who could satisfy the better taste she had acquired at Mansfield, whose character and manners could authorise a hope of the domestic happiness she had there learned to estimate, or put Edmund Bertram sufficiently out of her head."
Through Edmund's influence, Mary had acquired a "better taste" and "a hope of the domestic happiness", so she had learned to appreciate domestic happiness.
Earlier, in chapter 37, Fanny thought "the chance of Miss Crawford’s future improvement as nearly desperate", and that Edmund’s influence "would be finally wasted on her even in years of matrimony."
But the narrator suggests that Fanny was biased and inexperienced in her view --
"Experience might have hoped more for any young people so circumstanced, and impartiality would not have denied to Miss Crawford’s nature that participation of the general nature of women which would lead her to adopt the opinions of the man she loved and respected as her own."