In the third draft script Lucas actually wrote that Leia's screams are audible after the door slams down in the exterior shot of the cell. That detail disappeared in the later revisions; maybe it was too macabre.
The same script later describes her as "bloody and mutilated" when Luke and Han enter her cell, and she's unconscious, suspended upside-down in the air by some sort of electronic restraint. She doesn't seem to be too seriously harmed though, as she wakes up a couple scenes later and starts taking charge of the rescue as in the final film.
Lucas had a tendency to reuse language from earlier draft scripts even when it no longer made sense. The "bloody and mutilated" descriptor was originally applied in the second draft to Deak Starkiller, Luke's brother, who was so gravely injured that his life was in serious danger, and he remained unconscious for the rest of the film.
Still, Leia being unconscious in her cell makes more sense than an idea that appeared in one outline. Namely, Leia refuses to go along when Luke and Han rescue her, as she suspects Vader is trying to implicate her in a bogus escape attempt. Han doesn't want to take the time to argue with her, so he punches her in the face and knocks her out, after which Chewbacca carries her.
That idea is actually recycled from the very first draft, where it's Annikin Starkiller who punches Princess Leia Aquilae. By the end of the script those two are fully in love. So, weirdly, that outline with Han beating Leia up may be the moment where Lucas started to consider them seriously as an item.