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In theory they should but its off to a bad start. However, most houses have copper pipes now and not all reef keepers have problems.
Buy a test kit for copper and see how it is coming out the clean end, also be aware that the RO units lose effectiveness over time and will eventually start letting copper through. Just be aware that it could be a problem... A friend has copper pipes and an RO unit used for a huge reef tank and no problems with inverts