No, she shaved it to take a big $ movie role, knowing she had Alopecia and that by shaving her head there was a good chance it would grow back thinner than before, which it has. Many with Alopecia choose to wear a wig. Jada chooses to show her Alopecia for sympathy/fashion and can afford the highest quality of wigs and hairdressers if it truly bothered her. But fame is addicting and any attention is better than none.
When Chris Rock told the joke, Jada had a bemused little smile and Will Smith laughed out loud, it wasn't until Will laughing, looked at her that her face turned sour. It wasn't the joke that offended her, it was her husband laughing at her that hurt her feelings and it was then that his rage began. He placed the blame on Chris Rock, when the real problem is the Smith's marriage and relationship.