The top link is a study that shows that the improvement is pretty marginal in practice.

It does miss something: in specific ethnic enclaves SAT coaching is much more effective, perhaps because of a culture of out-of-school schoolwork and teaching beyond SAT prep. Those enclaves aren't particularly wealthy either (if I recall correctly it was a Korean enclave). Even then we're talking 70 points -- not nothing, but also not a radical transformation.