Technically it may be possible, but practically speaking it is unlikely to get approved and probably not worth pursuing.
Inmate marriage requests go through the warden's office and require administrative approval. Facilities are more inclined to accommodate marriage requests when the inmate is facing a long sentence and the union serves a meaningful purpose in terms of legal rights, visitation, or financial matters. When someone is a few months from walking out the door on work release, the facility's response is almost always going to be to wait.
Work release is the final stage before full reentry. He is already living with significantly more freedom than a standard inmate, going out to work and returning to the facility. That status puts him closer to the outside than the inside, and the facility is going to have little appetite for processing a marriage request for someone who will be home in December.
The honest advice is to save it for a real wedding. A few months is not long to wait, and getting married outside the walls with your family present, in a setting you actually choose, is worth that patience. A ceremony arranged through a work release facility is not the wedding either of you deserves when the alternative is just around the corner.
Plan the real thing. December will come faster than it feels right now.