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Mr. Nolan seemed like the type of guy who would side with Mr. Perry and tell Neil to listen to his father.
In the event of putting the blame on Mr. Keating, even if Neil had gone to Mr. Nolan as well, I still believe Mr. Nolan would put the blame on Mr. Keating regardless, still saying how Keating encouraged Neil to pursue.
Mr. Nolan doesn't strike me as a sympathetic person, so I don't believe Neil going to him would have changed Keating's fate.
It seemed like Neil wasn't the only one who's future was planned out for him by his father, as he called Charlie and Knox out when they tell him to stand up to his dad, explaining their path is to become a banker and a lawyer (I just rewatched this film the other day), so seeing father's pressuring their sons on a certain path probably was not an uncommon thing going on at that school.