So... Dwarfquisitor is going to be ex-Carta. That might make things rough with Varric. Will add some extra drama to the romance with Varric, if it exists. Regardless of Bianca's fate, the Carta was definitely to blame.
I was thinking about that too, so I think it would also depend on the age of the inquisitor. Hawke was in his/her 20s in DA2 and wasn't the warden around that age as well? Since Varric is in his early 40s and we assume that the Bianca thing ended in his late 20s (before the decade of Hawke), that would plug our quiizies around what? Maybe the Quizzy was like 10 when that happened? It wouldn't be his/her fault and I think Varric would just object to the Cadash family, not the inquisitor his/herself.
In which case a friendship or romance could happen, as long as there aren't really strong family ties? And that's even if the Cadash family had a big part to play with whatever happened to Bianca other than being part of the Carts.