As far as physically “working” I don’t know why it wouldn’t...provided you have the proper fireproof materials / required insulation under the copper. The copper should definitely pass as non-combustible.
As far as asthetically...definitely don’t plan on it staying bright and shiny. I would expect that the constant contact with pieces of firewood, ashes, heat and just general exposure to the atmosphere would eventually give it a patina similar to an old, dull copper penny. Not that this is necessarily a bad thing, just be aware of what the end result will be.
Corey