Structural functionalists believe that each part of society plays a role in keeping the society stable. Therefore, they would tend to argue that cultural deprivation contributes to this stability. They would argue that the achievement gap caused by cultural deprivation maintains the class and social structure of the United States.
A functionalist might argue that society is most stable when there is not much change from generation to generation. Parents' attitudes and cultural traits can be easily passed to children who will grow up to be like their parents. The achievement gap caused by cultural deprivation helps with this. Students who come from poor backgrounds do poorly in school. This helps cause them to remain poor. In this way, the cultural deprivation helps to perpetuate the culture of that class of people.
In this way, a functionalist can argue that cultural deprivation helps to keep society stable. It helps to do this by maintaining continuity and stability in our social structure.