Its a long-known, well-demonstrated effect on an individual level. A more likely causal mechanism than the kind of broad social effect in the reverse direction that you suggest is that access to quality education also affects experience with, patience with, and attitudes toward the kind of assessments used to measure IQ, thus influencing results.

(There's other wealth-related -- and, on a country-level, social-support-network related effects, too, as early childhood nutrition and other social-environment factors have an effect on IQ that, again, has been demonstrated on an individual level.)