If my son was arrested for possession of a firearm but there was no firearm on him, is that a legal charge?

You can possess things and not carry them around with you. For example, you may have a lawnmower in your possession, even if you are not pushing it, if it is in your garage .Your son should discuss the facts with his attorney, not to determine whether something is a "legal charge", but whether he is guilty of the crime.