Desire to make his brother more normal is part of the reason for the narrator’s treatment of his brother, and part of it is his determined personality.
It is hard to determine how people would react if circumstances had been different, but we can make inferences based on personality traits. You can describe the narrator (who is never named) based on the way he acts in this story.
First of all, the narrator definitely is strong-willed and determined. He wants to teach his brother to walk, and he does so when no one else thinks he can.
Doodle was five years old when I turned 13. I was embarrassed at having a brother of that age who couldn't walk, so I set out to teach him.
Notice, though, that he does not teach him out of brotherly love, but because he is embarrassed because Doodle is five and still can’t walk. It shows the narrator’s self-centeredness. I doubt this trait would change if his brother were “normal.” He probably would just find other ways in which his little brother embarrassed him. There is a large age gap between him.
Also, he does not seem to have much of an ability to show compassion. He leaves his brother behind when he gets frustrated with him, only showing emotion when he realizes he has contributed to his brother’s death.
We started home, trying to beat the storm. The lightning was near now. The faster I walked, the faster he walked, so I began to run.
The narrator does notice when Doodle collapses, and he does feel bad about it. He realizes that he is the cause. He pushed Doodle too far. I doubt that this would change. He probably would still push his brother if his brother could do more, he just would push him to do other things.
The narrator would probably give his brother a different nickname, since he didn’t like William Armstrong (maybe Billy), and would probably still dominate his life. I doubt that this narrator would ever give his brother peace. His basic personality traits would not change, even if Doodle’s did. He is not the type to ever be satisfied. He always wants more. When Doodle could walk, he wanted him to run. Hopefully if Doodle were a little stronger he could survive his brother.