Is there an implication that the father has many children with a variety of women, and therefore does not recognize a particular one? That would certainly be a reasonable situation in the American underclass, irrespective of race.
There is that implication, yes - as well as the implication that some parents don’t care about their kids.
Kids need active, involved parents in their lives. Preferably two of them, preferably one of each sex. I know this better than most. I was orphaned at nine. I was incredibly lucky that other adults voluntarily took on that role for me, in particular some of my teachers and some of the parents of my friends. You can get really screwed up if nobody is filling this role properly for you.