Not without executive emergency powers during the Great Depression that temporarily (we hope) suspend constitutional lawmaking itself. Read Ira Katznelson's new work "Fear Itself: The New Deal and the Origins of Our Time". Basically, it details how at every turn, New Deal legislation was passed only with caveats that kept the Southern racial system in place because of the Southern Senators and Congresspeople FDR needed for his Democratic majority, let alone to have his legislation come up in Congress. To end desegregation, Roosevelt (or Hughes) would have had to impose martial law for an extended period. and suspend constitutional government. And whose to say when if ever the constitution would ever be restored and under what circumstances?
Would African Americans then be identified with the forces of dictatorship or communism? How far to the Left would a government, such as that of Henry Wallace, that used martial law to ram civil rights down the South's throat at the point of a gun wind up going? Probably a lot further than most of it's leaders initially intended to go. It will make an interesting TL. Maybe a good novel.