I've seen even the strictest jurisdictions happily embrace the use of non-listed or unconventional raceway or conduit asemblies. The approval has come after I've explained the reasons for the use.
First, identify the reason you want to use a certain material, and outline your attempts to find a listed solution.
A starting point can be the UL "White Book." While the book might claim that, for example, there is listed conduit made of "miracle metal" or whatever material you wish to use, that doesnn't always mean you can buy it.
( I am thinking here of a pump manufacturer who needed some stainless RMC for a corrosive environment. While the UL provided a list of manufacturers, the electrical supply houses were not willing to supply it, and the manufacturers would only make it if the order was the equivalent of several freight-cars full. In the end, common stainless plumbing pipe was accepted by the AHJ).
The next step is to have a copy of some standard or specification. For example, the UL or ASTM standard for the product. Be prepared to show how your material meets or exceeds every requirement, save for the actual material. For example, is it as strong?
Show how the material you have chosen meets your requirements, while the usual product does not. For example, a certan plating shop in Chicago is able to use the (local law) expressly forbidden PVC conduit because any metal is quickly eaten through.
Finally, pay attention to the installation requirements. You might have to use additional supports, for example.
The biggest problems with using copper tubing as a conduit are the fabrication and the fittings. In detail:
1) Try bending it and it tends to collapse- not allowed;
2) The radius of the elbows is far too tight for wiring- you must be able to pull the wires; and,
3) Connections are not allowed to rely upon solder alone for mechanical strength.
So, what's one to do? Well, I once met the exact same problem - the desire to make the EMT fit in with the copper piping and other architectural details - using spray paint. There are metallic paints at the hardware store that are spot-on matches for copper, brass, whatever you want to use. In other situations, you can probably get away having the materials plated