With no explanation, label text_A→text_B with either "DON'T KNOW", "NO" or "YES".
text_A: Sarek supported Spock's scientific learning and application to the Vulcan Science Academy, as mentioned in "Journey to Babel". In the 2009 film "Star Trek", Spock rejects his acceptance into the Vulcan Science Academy on the basis that they would never fully accept someone who was only half-Vulcan. Although this film set the Kelvin timeline scene in this and later films, writer Roberto Orci stated that he felt that the actions were orthogonal to the changes in this timeline and so would have occurred in the same manner prior to "The Original Series". Because Spock did not enter the VSA and sought to join Starfleet instead, he did not speak to his father for the following 18 years.
text_B: Might Sarek tell Spock in the original timeline that he was accepted to the Vulcan Science Academy?
YES.