But I don't think that Anne was being consciously faithful to Frederick or decided that if she can't marry him, she won't marry at all. in chap 4, it also says --

"time had softened down much, perhaps nearly all of peculiar attachment to him, but she had been too dependant on time alone ... No one had ever come within the Kellynch circle, who could bear a comparison with Frederick Wentworth, as he stood in her memory. No second attachment ... had been possible to the nice tone of her mind, the fastidiousness of her taste, in the small limits of the society around them."