Seems unlikely . . . If they did and you win, that would give you a potential malicious prosecution claim. I am not sure a petition for factual innocence will apply to an arrest record, especially if you were never charged.
With all due respect to the previous answer....
A petition for factual innocence does seal and destroy arrest records if granted. That's the whole purpose.
Read Penal Code section 851.8. You can make your application at any time, but the response time is linked to the statute of limitations. The police has 60 days from the end of the statute of limitations to respond to your request before you can file the motion in Superior Court. This ensures that charges cannot and will not be filed before you undergo your motion.
As Mr. Dane notes, in cases where charges are not filed, you have to petition the law enforcement agency first. If they deny your petition, you can file in the Superior Court.
However, if there were no charges filed, there is no public record of your arrest. Your "rap sheet" is not a public record.
If your petition to the law enforcement agency is denied, and you then file a petition in the Superior Court, that filing will be a public record. If the court denies your petition, the court records become a permanent, public record of the arrest... when there wouldn't otherwise be one.
That's why a petition for factual innocence, under some circumstances, might do more harm than good.