“I certainly shall not. You know how I detest it, unless I am particularly acquainted with my partner. At such an assembly as this it would be insupportable. Your sisters are engaged, and there is not another woman in the room whom it would not be a punishment to me to stand up with." (Chapter 3)

Although the SS may believe along with Darcy that the company is insupportable they seem to be powerless or unwilling to act upon it by not dancing. When Bingley tells Darcy to dance and not stand about in that stupid manner Darcy replies that his sisters are both engaged so they are obviously dancing at least with one local gentleman as Mr. Hurst could only be dancing with one of them; since there is no indication that Mr. Hurst is or is not one of their partners they could each be dancing with a local gentleman. In short, I do not think Darcy attended the assembly only to dance with the Caroline or Louisa. Why he came is an interesting question. From Darcy’s manner it does not seem he ever enjoys himself so for me his behavior casts serious doubts that he came for pleasure of any kind. I think he attended the assembly because his host and friend, Bingley, was attending the assembly. It was a duty to him and performed with little if any graciousness at all. ;D