that's the point isn't it though? Anne De B is there to provide evidence that Darcy's aristocratic relatives are not as wonderful as he would like to think that they are. His aunt is jsut as vulgar and ill bred and stupid as Mrs Bennet, and his cousin has no social skills...
Darcy has probably overlooked his aunt and cousin's failings previously but with Eliz htere, he begins ot realise just how awful they are. He too has embarrassing and stupid relations... being well born is no guarantee of intelligence or charm or proper behaviour...
So I Dont think that Anne has hidden depths... I think that she IS unaccomplished, stupid, dull, virtually unable to socialise and problaby in her own way jsut as haughty as Lady C.
and possibly, that's why while Anne problaby has SOME poor health, Lady C has never apparently taken her to London or to Court, and is I suspect hoping desperately taht Darcy will feel obliged to marry her... because otherwise how is she going to get the girl off her hands?