In the Court of Owls, Batman
is stabbed in the back and the blade protruded through his stomach
I'm sure in the real world he couldn't have defeated the bad guy after that. But is it even possible that he survived ?
Yes and no. It boils down to two questions: did any vital organs/intestines get scratched/punctured, and how long did he have to wait before he had medical attention. The first answer will to a degree affect the second one of course.
But yea, it's dangerous and painful but ultimately survivable if there is no massive trauma and he seeks a surgeon immediately.
Edit: of course I say this not seeing the image of it being done to better judge the extent of damage.
Edit: the image now being posted, that looks less like Batman and more like Batwerewolf so now that's a different game entirely that you can't really judge.
Batman has above peak human durability (without being supernaturally though), taking blows from Wonder Woman and Azazel and surviving.
Warning! Some disturbing images in those two links.
So yes, he can definitely survive the wounds he suffers in Court of owls.