You are lucky because you actually live in a state that after your case has been expunged, the law makes it untraceable. The New Jersey Criminal Code allows a person who has been arrested or convicted of a crime to make submission for an "Expungement". An Expungement is a legal procedure that "removes" a criminal record from the files and computer systems of the Court, police department and other law enforcement agencies.
When an expungement is approved, law enforcement agencies are required by law to keep that person’s records private. However, the law does allow expunged records to be used later in certain cases. Many people want to go through the expungement process so that they can have clear records when they apply for jobs. However, the law does allow expunged records to be used when a person applies for an occupation with a law enforcement agency. This includes careers with state, county, and local corrections departments, prosecutors, courts, and police. This does not mean that those agencies will never employ people with records, but it does mean that those applying must still reveal the existence of an expunged record on a job application.
The expungement process is available to help people to erase a mistake of their past so that it will not effect their future. The expungement statute within the State of New Jersey allows you to reverse time and expunge that mistake as though it had never occurred.
That being said, if the youth program does perform the background check on you and your misdemeanor has been expunged, your background record should come up clean, since the New Jersey law requires that the crime be erased. However, there is still a chance that if it is the government that does your background check, there is a possibility that they could find it, because they are the government. If it ever comes into questions, Federal Law always mandates over State Law. However, the New Jersey law that is in effect should protect you.
I am giving you a link with answers to multiple questions that you may have also about expungement in New Jersey.