Yes, I think that Chris Brown will learn lessons from his 30-day incarceration, because he will learn that he does not like being locked up. Brown will get a taste of jail and hopefully realize that he does not ever want to be back there. Brown will know what it is like to be with general criminals and not be a star.
I think Chris Brown will learn that there are consequences for your actions, even if you are rich and famous. There is just so much misbehavior you can take part in before you have to pay the piper, just like everyone else. He definitely has some anger management and entitlement issues and hopefully some time under strict controls will help manage that.
I think Chris Brown will say that he's learned his lesson, but I don't think it will ultimately change his behavior. He seems to have a pattern of abusive behavior and combined with his fame and money, I'm sure he'll repeat it. Also, I don't think our system is built to rehabilitate, being incarcerated is a punishment, but not enough of a deterrent to prevent future bad acts.
I think that Chris Brown will not learn any valuable lesson from his 30-day incarceration because his problem is mental. He is suffering from bipolar disorder and being in jail is doing nothing to get him treated and back on the right track. He needs counseling and medication and help until he accepts and has his issues under control.