If NBC had bought Star Trek
as a series based on "The Cage" it's still possible Roddenberry could have made further changes before going into series production. We just have no idea what those changes might have entailed. "The Cage" is in many ways a rough draft, a first effort. NBC liking "The Cage" but wanting changes and then asking for a second pilot forced Roddenberry to make changes. Jeffrey Hunter choosing not to return also forced Roddenberry to make changes with his lead character. As a result he not only changed the actor he also changed the character's name and consequently that changed the character's personality. And in extent in changed the overall feel of the show.
Jeffrey Hunter was more the classical type of Hollywood leading man. He was very clean cut with defined features and somewhat of a more reserved bearing in his portrayal of Pike. William Shatner was somewhat more everyman (albeit still handsome) in appearance and more expressive in his portrayal of Kirk. Eliminating Number One and making Spock the "emotionless" one played off well with Kirk's more outgoing nature. It wouldn't have played the same with Pike who was also somewhat reserved. And having Spock reserved made Number One redundant, so goodbye.
We''ll never know how well TOS might have done if they had gone forward into production based on "The Cage." We can only speculate.