I know you did not ask how to stop the bully from being a bully but that you want to know how you can force the injured one to survive. There is no way to tell if he will survive, just give it the best care and be sure it has warmth.
About the part about chicks being fun, they are fun but they are also animals and animals don't subscribe to human thinking. They are simply animals and have some strange habits and instincts and if they see blood, it drives them to produce more blood. Who knows, that may even be an instinct for eating each other just in case the food source stops.
It could be the bully got an overdose of survival instincts that is driving it to seek food by pecking everything that moves. In my opinion, the only way in a brooder to stop it quick is to trim the upper beak. Not sure how effective distasteful products will be and how long you would need to smear them on BUT, in commercial operations (which some consider cruel--but you don't have to be as drastic) they almost treat the animals as if they are also animals themselves by stopping the ability of the chickens to practice survival on their sisters.
About the part about chicks being fun, they are fun but they are also animals and animals don't subscribe to human thinking. They are simply animals and have some strange habits and instincts and if they see blood, it drives them to produce more blood. Who knows, that may even be an instinct for eating each other just in case the food source stops.
It could be the bully got an overdose of survival instincts that is driving it to seek food by pecking everything that moves. In my opinion, the only way in a brooder to stop it quick is to trim the upper beak. Not sure how effective distasteful products will be and how long you would need to smear them on BUT, in commercial operations (which some consider cruel--but you don't have to be as drastic) they almost treat the animals as if they are also animals themselves by stopping the ability of the chickens to practice survival on their sisters.