As a science term for "white", see "Too Many Scientists Still Say Caucasian" in Scientific American, also "Abandoning the word Caucasian" in the Journal of Genetic Counciling and "The Ongoing Incorrect Use of Caucasian in Medical Research" in the journal Health Equity. There are a bunch of scientists who think this.
I think if you are actually describing something or someone from the actual Caucasus mountain region, it would be correct, but people might thing you meant "white" so even then you might be better off with "from the Caucasus Mountains".