Yes and No. Years ago there was a comprehensive study done where they placed children of a lower IQ race into the households of a higher IQ family who adopted the children and raised them as their own. They also took some high IQ Asian children and put them in a lower echelon IQ family. After a number of years, the scientists retested the children.

To the scientists surprise, the children of higher IQs raised in lower IQ household still scored just as high on the achievement tests.

Likewise, the low IQ children who were placed and raised in a high IQ household with all the privileges, scored no higher on the tests than their impoverished counterparts in their home countries.

So, based on this, there is a genetic component that cannot be overcome by environment, schooling and diet choices.