I do not think she has any intention of going, she knows Sir Walter and Elizabeth will say what they do. But it might be expected (for example by Lady Russell and others) that she go now that Anne is there so she does this for formality's sake. It puts her relationship with Sir Walter and Elizabeth on a slightly different plane - she is now there by express invitation as a guest, having been 'persuaded' to stay, whereas there was an element of the paid companion before (though I do not think she was paid).