Well, we know how well that worked since he simply recast her as another more friendly (and less in the forefront) character later.Unfortunately, no. Before being given the go-ahead for the second pilot, NBC gave Roddenberry a list of things they wanted changed from the original pilot. Among them was no female first officer.
I'm pretty sure that the memo had nothing to do with the first officer being female. They just wanted Gene to cut Majel loose.
But aside from the idea that NBC may have disapproved of Roddenberry casting his girlfriend as the ship's second banana, early screenings of "The Cage" revealed that test audiences--particularly women--responded rather negatively to Number One. They just didn't like the character, which was reason enough for NBC to want her gone.
The infamous NBC memo also told Roddenberry to get rid of "the guy with the funny ears" too.
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NBC truly did want to get rid of the Spock character, but the thing about Number One is a myth. Countless sources confirm this in Inside Star Trek: The Real Story, as well as Joel Engel's biography of Roddenberry. NBC wanted a name in the role, Roddenberry wanted his no-name mistress (who, moreover, NBC didn't care for as an actress).
That's why there's no female first officer going forward. Roddenberry dropped the role rather than re-cast it.