Depends on how you look at copper.
I am a faceter of gemstones and I would not facet a piece of copper, be it native or not. A gem is a stone that is clear to opaque and one that has a brilliance of its own when cut properly.
Native copper, beautiful as it is, is a specimen. Specimens are a rock or mineral taken from the ground that has its own unique qualities in its natural form. Yes, some specimens such as quartz, tourmaline and emeralds may start as a specimen when displayed in their natural form. They can then become a “gem”, after faceting, with flash, fire and brilliance.
In the case of Sunstone, it is a feldspar but two very different types can be found… the Oregon Sunstone is a true gem, with is’s clarity and colorization. Although some may say yes… I do not consider the sunstone from India a gem as it is not clear because of hematite particles in it, vastly restricting its clarity and brilliance.
While a quartz crystal can be a beautiful gem when the specimen is clear with no inclusions, (yes, for you out there thinking quartz with rutile inclusions can be stunning, for the sake of my point, I am leaving that out!), milky quartz or quartz with micro cracks in it may make a fantastic specimen,but that same piece would be a lousy gem.
In short, having dug up native copper myself, being originally from Upper Michigan, copper is a wonderful looking specimen, but I would not call it a gem…In my humble opinion!