There are several methodological issues with analyzing the question. The first is the definition of African American that becomes increasingly problematic as assimilation increases. Increasing interracial marriage (along with earlier miscegenation) makes the category itself problematic.
In one way, it is possible to say that African Americans have assimilated successfully at all levels of society. The current President of the United States, Barak Obama, is an African American, as are such noted figures as Tiger Woods (golfer), Oprah Winfrey (popular media), Condoleeza Rice (past Secretary of State), and Toni Morrison (novelist).
On the other hand, many neighborhoods and schools still remain segregated by ethnicity, and statistically, African Americans lag behind all other US ethnic groups on such measures as infant mortality, life expectancy, income, and education.