Zoltan Hajnal says no:
bq. What implications does the growing economic divide between poor and middle class blacks have for the political arena? Traditional accounts suggest that increased economic diversity should lead to increased political division as the middle class becomes more conservative. Others maintain that race will continue to trump class because of ongoing racial inequality and widespread racial discrimination. I argue for a third alternative. I suggest that for blacks and possibly for other racial minorities increasing class status reinforces race. Class gains may increase the salience of race because economic success often means working in a predominantly white world and experiencing discrimination more regularly. I test these theories using the vote in direct democracy. I find that middle class blacks are more rather than less likely to support a liberal or black agenda. Class works differently for African Americans than for whites.
The published paper is here (gated). A final draft version is here (in MS Word). The data are from a pooled set of Los Angeles Times exit polls in California, which produces an unusually large sample of African-Americans.
If this article’s conclusions are correct, the future economic advancement of blacks will not necessarily lead them to a more conservative politics.