Up to the point of the marriage proposal, does Elizabeth legitimately care about Darcy's opinion and feelings towards her in Pride and Prejudice?
First let's remember that there were two separate instances of proposal between Darcy and Elizabeth in Pride and Prejudice. Also, the states of mind of both Elizabeth and Darcy are entirely different on each occasion.
The first proposal occurs in chapter 34. By this time, Elizabeth was greatly prejudiced against Darcy after learning that the latter had been responsible for the sudden chasm between Mr. Bingley and Elizabeth's sister, Jane. This separation had caused a great pain to Jane, who saw her marriage prospects nullified.
Mr. Darcy's shameful boast of what misery he had been able to inflict, gave her a keener sense of her sister's sufferings.
The combination of Jane's sadness, and her (Jane's) potentially abysmal future as a spinster without a dowry, propelled Elizabeth into a rage against Darcy. This anger was even more aggravated when Darcy dashes toward Elizabeth and obliviously declares his love for her.
While his words at the time are romantic "enough"--he does declare that he admires Elizabeth-- he commits the tomfoolery of expressing, with brutal honesty, his condescending sentiments toward Elizabeth's family, and the fact that he feels that separating her sister from his friend Bingley was actually an act of kindness. Yes. Darcy's idea for a marriage proposal was to declare his admiration and then remind Elizabeth that she is still a social inferior.
Yet, way before he said those words, which deeply piqued Elizabeth's rancor, Elizabeth had already had her say about whether she cares if she is admired by Darcy or not.
I have never desired your good opinion, and you have certainly bestowed it most unwillingly.[...]The feelings which, you tell me, have long prevented the acknowledgment of your regard, can have little difficulty in overcoming it after this explanation.
Basically, at this point, Elizabeth could care less what Darcy thinks of her because she has already made an opinion about him which is far from favorable. If anything, any dislike for her would match her own dislike for him, and both would be on the same note.
However, this changes throughout the novel. Darcy will eventually disclose the truth about Wickham, which changes Elizabeth's opinion about many things, including her opinion of Darcy. At that point, Darcy and Elizabeth enter a cordial period. However, this abruptly ends when Elizabeth finds out via Jane that Wickham and Lydia have eloped.
This is when Elizabeth starts caring about Darcy's views and opinion of her, because what Wickham and Lydia do brings deep shame to any family and ruins their name and repute.
A young, single lady eloping with a man without marrying denotes that the woman had been let loose without any discipline or control. In turn, this means that the family is careless and dysfunctional. Keep in mind that the Bennetts showed their true, semi chaotic colors at the Netherfield ball in chapter 18, where Elizabeth was way beyond embarrassed by the coarse behaviors of her family members:
to Elizabeth it appeared, that had her family made an agrement to expose themselves as much as they could during the evening, it would have been impossible for them to play their parts with more spirit, or finer success
Deep inside, Elizabeth admits that her family is wild. Yet, by the time that she starts building a good opinion of Darcy, her family name is about to be potentially ruined, and the actions of Lydia will possibly reflect on her, being that she is her sister. This is when Darcy abruptly leaves Elizabeth's presence when he visits her at the Gardiners (chapter 45), and Elizabeth believes that this is because he feels ashamed of her. This time, she does care about what Darcy thinks about her.
Eventually, we learn that Darcy went after Wickham to force him to do the right and restitute the Bennett's good name by marrying Lydia. All of this makes Elizabeth realized that, while she was prejudiced against Darcy once, he is indeed a good man, after all. He is just a very proud man (hence, the title of the novel).
By the time the second marriage proposal comes in Longbourne (chapter 58), Elizabeth and Darcy are no longer prejudiced against one another and they agree to marry.