Here is what LEOSA says about who is covered under the law:
In order to be covered as a "qualified law enforcement officer," a person must meet each and every one of the following criteria: He or she must be (1) "an employee of a governmental agency"; (2) "is authorized by law to engage in or supervise the prevention, detection, investigation, or prosecution of, or the incarceration of any person for, any violation of law"; (3) has "statutory powers of arrest"; (4) "is authorized by the agency to carry a firearm"; (5) "is not the subject of any disciplinary action by the agency"; (6) "meets standards, if any, established by the agency which require the employee to regularly qualify in the use of a firearm"; and (7) "is not prohibited by Federal law from receiving a firearm." In addition, the privilege conferred by the law applies only when the individual "is not under the influence of alcohol or another intoxicating or hallucinatory drug or substance.
Based on what it says here, the law seems to make no distinction between volunteer and full time paid officers, which would make it seem as if volunteers are indeed covered by it. However, IANAL, and this is not legal advice, so proceed with caution.
Any society that would give up a little liberty to gain a little security will deserve neither and lose both.
Benjamin Franklin