It depends.

Kids who score high but who started with a low-quality curriculum will score higher once they go into a high quality education environment.

If they already have a maxed out environment, then I would not expect to see much of a change.

Test anxiety may also be a factor to bump up scores.

SAT and ACT do correlate to IQ, all things being equal, but you need time to work things out you do not know - esp on the harder questions in the math and verbal sections.