No, Schoolboy Q has not quit rap. He released his new album, titled "Blank Face" on July 8, 2016 and is currently touring. However, in an interview he mentioned that he almost decided to quit rap due to his struggles with fame. Since he has just released a new album, it can be assumed that he will be around for a while longer.
Rap musicians are less about music then they are about creating noise for themselves. Pretending to walk away is just another way to call attention to himself and draw fans out to tell him how much they love him and his music. When he goes back on tour, or releases another album, sales will be through the roof.
No, someone who's been doing this a while as his career will not quit for good. He may be taking a break. He may be changing his branding. He may be expanding his repertoire. He may even be changing his message. However, I don't think he's left the genre altogether, at least not for forever.
When someone get's so good at a field that it's all they do for a living (Music production, Computer Programming, and more), it gets difficult to just quit, especially after they have been doing it for a long time, and it's what they LIKE doing. Schoolboy Q is not done yet.