Sort of- it is implied that a woman gets sexual pleasure from "petting a cat", but it is not graphic, it is a metaphor for masturbation. Still, it might make some people uncomfortable since there is a real cat in the story.
Throughout the chapter "SEETHECATITGOESMEOWMEOW-COMEANDPLAYCOMEPLAYWITHJANETHEKITTENWILLNOTPLAYPLAYPLAYPLA" a cat is abused by a child envious of his mother's affections to it and not him.
It is implied that Pecola's father may be mentally ill, and he rapes his daughter and beats his wife. He goes "mad", and it is implied that the beatings and rape are his drunken way of showing love.