I am in the process of AOS now. As I have the same question as you, I have checked so many information online. Unfortunately, there is not much information mentioning can K visa go to school? I recently found the answer from ICE that wrote '' Nonimmigrants: who can study ? ''.
And it shows k visa principle may attend school.
The information was written in 2018 but this information is from the government. I think it is good news for applicants 😃