If he was cited, it's unlikely the judge will take him into custody for the offense at arraignment.
Penal Code 22210 is a new statute, making it illegal to possess, among other things, a billy club. (That offense, and several others, used to be contained in Penal Code 12021.) It is a "wobbler," meaning it can be charged as a misdemeanor, with up to a year in jail, or a felony that carries up to three years in jail. (The time for a felony would be served if the defendant has a prior "strike" felony or is a registered sex offender. It was a state prison felony for everyone until a legislative amendment on June 28, 2012.)
For your son to be convicted, the District Attorney would have to prove that he intended to use the bat as a weapon. That may be difficult, unless your son blabbed that he had the bat for protection.
(Tip: always politely decline to answer police questions without an attorney present, and always carry a ball and glove if you have a bat in your car.)
The search of your son's car may also have been illegal, which could lead to suppression of the baseball bat.
Bottom line: Your son needs a good lawyer to sort this out. If you can't afford to hire a private attorney, the judge will appoint one of the excellent attorneys in Alameda County Public Defender's Office.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like this site, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.
Unless there are unusual circumstances, it is unlikely that your son would be put in jail at his court appearance. He was cited and released without bail, so he should remain out of custody as long as he shows up for his court dates. Your son needs an attorney. If he cannot afford to hire an attorney, the court will appoint counsel to represent him. Feel free to contact me to discuss your son's case. Good luck to you.
Your son should say nothing else to anyone. Nor should you repeat anything e;se. You or your son should retain counsel to represent him. Mr. Marshall and Mr. pullman are very fine attorneys as are Mr. Kaman and Mr. Feasel . All are listed on AVVO and in the bay area. [ Mr. Marshall is in Chico but maybe you can convince him to come to the bat=y area for the climate.]
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.