Playwright Paul Rudnick says she did - and gives her a charmingly rueful characterization based on her savvy sense of her own "difference" in the image-driven world of Ludwig's court. Indeed, perversely enough, it's her very awareness of her lack of conventional beauty - her incipient sense of camp - that endears her to the gay Ludwig.
But is Rudnick exaggerating what may have only been a slight abnormality? The photographic evidence for said hump is slim - of course the photos may have been doctored; but Sophie looks pretty normal above, in a photograph with Ludwig taken during their engagement. (For more images of Sophie, check here.)
Born Sophie Charlotte Augustine de Wittelsbach, Sophie was officially a Duchess of Bavaria; an alliance with Ludwig would have been a big step up, and would have put her on a nearly-equal social footing with her sister, Elisabeth, who was now Empress of Austria and had also been close friends with Ludwig. Clearly, unlike the character she inspired in Valhalla, Sophie was serious about the matrimonial sweepstakes; she married Ferdinand Philippe Marie, duc d'Alençon, in 1868, the year after she was dumped by Ludwig, and promptly had two children. So no flies on her, hump or not.
One last note about the gallant Duchesse d'Alençon. She was caught in a famous fire, at a charity bazaar in Paris in 1897; but when rescuers tried to carry her away from the flames, she insisted other women and children be saved first, stating "Because of my title I was the first to enter here, and I shall be the last to go out." Sophie perished in the subsequent inferno, at age 50.