I doubt it, at least in a first past the post system. No matter how much the establishment political parties alienate the African-American community, they're not a majority in any US state and running their own party on black issues is essentially throwing their vote away. Even if they support a third party en masse, such a party needs to try to appeal to disaffected white voters as well to have any hope of winning.
In some democracies (I'm thinking especially Israel, but I'm sure there are others) ethnic parties can win heavily among their ethnicity, join a coalition, and thereby have influence in government. But the electoral system in the US strongly discourages ethnic-based political parties at a national level, because candidates can win with a plurality of the vote, which encourages consolidation into two or sometimes three political parties. And African-Americans aren't numerous enough as a percentage of the electorate to dominate one of those two or three parties at a national level.