I would not expect computers and/or computer science to improve the performance of students in SAT Mathematics, AP Calculus, and AP Statistics.
We use computers so we dont have to remember all that crap. The computer does the math.
I would expect it to improve reading, reading comprehension, written language skills, and logical thinking. That is what the student is learning!
Computing teaches any problem domain that you are asked to code solutions for.
The problem with initiatives like code.org is that they generally try to engage kids by making things move on the screen. Most of that means doing very basic arithmetic in an esoteric firmat surrounded by Byzantine library calls.
If you want kids to do better in statistics, you shouldn't start with the paradigm of interactive entertainment, but with the far less abstract view of a computer as something that computes stuff. Kids might not like their schoolwork, but it's certainly relevant to them. Part of the problem teaching complex maths is that the mechanics of carrying out the underlying computations diverts attention from the "big picture" view. Procedural computing was designed specifically to address the problem of "can't see the wood for the trees" by separating the general algorithm from the specifics of implementation.