It's True. The Democrats needed the African American vote, so they promised jobs under FDR's New Deal. The African Americans didn't like getting in bed with the enemy, but felt they had no choice.
Bringing up FDR… FDR also needed to reach out to African Americans for a blunt reason.. as "cannon fodder" for WW2.
Up until WW2, blacks and women were subjugated to being 2nd class citizens. Women typically did not work until WW2 in which the men went off to fight and the women had to work in factories to make the munitions for the war. Google "Rosie the riveter"