Probably make it very dark. As a very coarse rule of thumb, the better the conductor for a piece that runs the full circumference of the coil, the darker it'll make the sound.
For my Tbird pickups, even a brass cover took all the life out of the sound. Copper should be even worse because of the higher conductivity. Unless you are looking for a very dark tone, I don't think you'll be pleased with the result. You could test it pretty quickly by wrapping the pickup with the copper shielding tape they use for control cavities. An actual copper can will sound even muddier due to the greater thickness.
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