What is a common core standard to one individual, may not be a common core standard to another student. So making these supposed changes may or may not help the outcome of the SAT test. No doubt there are thoughtful, tricky questions on the SAT and to pave them down to a "Common Core" would almost be impossible.
Common Core standards and activities have long since been shown to be flawed, and in many schools have resulted in serious problems. The shift to make the SAT reflective of Common Core standards only demonstrates that educational monopolies are trying to ensure their own survival by coordinating with each other.
Changes to the SAT test based on Common Core standards will not do much to improve how well students perform on the test. Some students are just not good test-takers. No amount of tweaking is going to improve how well students do on the SAT. Instead, schools should focus more on teaching students how to think.
No, changing the SAT to fit common core standards will not help students do well on the test because Common Core isn't something that a lot of students do well with. Common Core is a great way to make everyone equally bad, but if you don't get it, you're not going to get it on a test either. It's not helpful.