He can always sue that's not the real question. The real question is will he prevail once he sues and the answer to that is probably not.
First he will have to go to trial and be found innocent and then the facts have to be very weak to sue for false arrest. Also the basis to violate him on probation is much less than it takes to convict him of the new charges.
My name is Stephen R. Cohen and have practiced since 1974. I practice in Los Angeles and Orange County, CA. These answers do not create an attorney client relationship. My answers may offend I believe in telling the truth, I use common sense as well as the law. Other state's laws may differ.. There are a lot of really good attorneys on this site, I will do limited appearances which are preparation of court documents it is , less expensive. However generally I believe an attorney is better than none.
Who does he want to sue? The judge that found probable cause, the cop that believed he had PC, the PO who put out a warrant based on a new law violation? has you son been acquitted of the new arrest? There is a little thing called sovereign immunity that will probably apply. I agree with Mr. Hornsby, highly unlikely.