The short answer: Yes. We are told so by the omniscient narrator.
The long answer: We have this paragraph explaining Darcy’s intentions, it does change from Elizabeth’s perspective to narration, but Jane Austen does that frequently.
In Darcy’s presence she dared not mention Wickham’s name (Narration); but Elizabeth instantly comprehended that he was uppermost in her thoughts; and the various recollections connected with him gave her a moment’s distress; but exerting herself vigorously to repel the ill-natured attack, she presently answered the question in a tolerably detached tone. While she spoke, an involuntary glance showed her Darcy, with a heightened complexion, earnestly looking at her, and his sister overcome with confusion, and unable to lift up her eyes. (Elizabeth’s POV) Had Miss Bingley known what pain she was then giving her beloved friend, she undoubtedly would have refrained from the hint; but she had merely intended to discompose Elizabeth by bringing forward the idea of a man to whom she believed her partial, to make her betray a sensibility which might injure her in Darcy’s opinion, and, perhaps, to remind the latter of all the follies and absurdities by which some part of her family were connected with that corps. (This explanation is NOT from Elizabeth’s POV; it is either Caroline or the narrator) Not a syllable had ever reached her of Miss Darcy’s meditated elopement. To no creature had it been revealed, where secrecy was possible, except to Elizabeth; and from all Bingley’s connections her brother was particularly anxious to conceal it, from the very wish which Elizabeth had long ago attributed to him, of their becoming hereafter her own. He had certainly formed such a plan, and without meaning that it should affect his endeavour to separate him from Miss Bennet, it is probable that it might add something to his lively concern for the welfare of his friend. (This is narration. While Elizabeth may suspect most of this information, we are told it as a positive fact)
(Alternative reading: It is also possible to read this entire paragraph as narration. And yes, the narrator is sassy and sarcastic, that’s our Jane Austen)
Let’s examine another paragraph that switches from Elizabeth’s perspective to narration, we will see the same technique:
Elizabeth listened in silence, but was not convinced; their behaviour at the assembly had not been calculated to please in general; and with more quickness of observation and less pliancy of temper than her sister, and with a judgment too unassailed by any attention to herself, she was very little disposed to approve them. (Elizabeth’s POV) They were in fact very fine ladies; not deficient in good humour when they were pleased, nor in the power of being agreeable where they chose it; but proud and conceited. They were rather handsome, had been educated in one of the first private seminaries in town, had a fortune of twenty thousand pounds, were in the habit of spending more than they ought, and of associating with people of rank; and were therefore in every respect entitled to think well of themselves, and meanly of others. They were of a respectable family in the north of England; a circumstance more deeply impressed on their memories than that their brother’s fortune and their own had been acquired by trade. (This is very clearly narration; Elizabeth would not know this information)
We have three additional hints at Darcy’s intentions, one is in the post-proposal letter:
That I was desirous of believing her indifferent is certain—but I will venture to say that my investigation and decisions are not usually influenced by my hopes or fears. I did not believe her to be indifferent because I wished it; I believed it on impartial conviction, as truly as I wished it in reason.
Darcy’s “hopes or fears” alludes to his hope that Bingley would be connected to his family by marrying Georgiana. (Extra note: how arrogant is Darcy for thinking that he can be unbiased! What a guy.)
Hint 2 is Caroline’s Bingley’s sanguine hopes about Bingley marrying Georgiana.
Mr. Darcy is impatient to see his sister; and, to confess the truth, we are scarcely less eager to meet her again…
Caroline may be a bit over the top in her pursuit of Darcy, but she’s no idiot. The Bingley sisters are socially adept: “Their powers of conversation were considerable. They could describe an entertainment with accuracy, relate an anecdote with humour, and laugh at their acquaintance with spirit.” I would not discount this letter as Caroline’s wishes alone because…
Hint 3 is how much time Darcy and Bingley are spending together, and with Georgiana:
“and from knowing them to have been together the whole of last summer.”
“But, though this might be imaginary, she could not be deceived as to his behaviour to Miss Darcy, who had been set up as a rival to Jane. No look appeared on either side that spoke particular regard. Nothing occurred between them that could justify the hopes of his sister.”
Georgiana Darcy does not yet seem to be “out” and yet, Darcy has spent the summer, half of the fall (at Netherfield), and then a considerable length of time in the winter with Bingley and often Georgiana has been present. This is the kind of “throwing together” that we might expect out of Mrs. Bennet!
Lastly, why would Darcy allow this? Isn’t he a snob who wants a family of superior connection for his sister, Maybe. But we also know that Darcy is a loving brother/guardian, even Wickham admits this. We also know that Bingley is a super nice guy. Finally, not all “trade” is equal and we have plenty of evidence in the text that the Bingleys and the Gardiners, for example, are viewed as different in class:
We are told that the Bingleys have a habit of “associating with people of rank”. Which means that people of rank have agreed to associate with them.
Mrs. Gardiner admits, “We live in so different a part of town, all our connections are so different.” They are not associating with the same people as the Bingleys.
The Bingleys live as if they are gentry class, “but as he was now provided with a good house and the liberty of a manor“
The Gardiners live as people who work “lived by trade, and within view of his own warehouses”
All of the Bingleys have a gentleman/woman’s education, the sisters “had been educated in one of the first private seminaries in town”
Mr. Gardiner might be able to put his children in a similar position, but Mr. Gardiner is from trade.
Bingley himself has never worked a day in his life, he lives off the income of his inheritance. “Mr. Bingley inherited property to the amount of nearly a hundred thousand pounds from his father, who had intended to purchase an estate, but did not live to do it.
Lastly, things are much more fluid, in Jane Austen’s works, than modern people like to portray. Emma is a massive snob, but she accepts Mr. Weston as an acceptable person to visit. Mr. Weston, “quitted the militia and engaged in trade”. And yet, once he purchases his small estate of Randalls, Emma will visit him and happily see her former governess married to him. Emma also teaches us to fake it till you make it, “There can be no doubt of your being a gentleman’s daughter, and you must support your claim to that station by every thing within your own power, or there will be plenty of people who would take pleasure in degrading you.”
This is important to consider when we think of the Bingleys. I have no doubt that they would never tell anyone about their unfortunate relations who remain in trade. They have left that world behind and do everything they can (such as paying for education) to make themselves look like gentry. Mr. Gardiner, on the other hand, is not doing that. And Elizabeth, unsnobby as she is, does not ignore the parts of her family that are below her class. While it seems strange to us, it seems like Mrs. Bennet should have cut off all contact with the Phillips and the Gardiners if she wanted to be seen as more respectable. (Lucy Steele, who has a lower background, does this in Sense & Sensibility)