Unrelated to the genealogy; but at what point does it become ridiculous to claim yourself a prince? With over a century of no power for the family and no obvious way back to it as the kingdom is well dissolved, it feels like dress-up to style yourself a prince.
I don’t want to cast doubt on his claims either, but I was unable to find anyone with the surname Kopaliani in any of the main or cadet branches of the house of Bagrationi.
Maybe ridiculous, but not totally unprecedented. Aga Khan IV is generally considered to be royalty despite the fact that his family hasn't held secular power (outside of the occasional governorship) since [1095](https://en.wikipedia.org/wiki/Nizar_ibn_al-Mustansir). Of course, they held religious leadership as Imams of the Nizari branch of Islam.
Very quickly, considering the monarchs of Denmark and Sweden removed titles from grand children of the reigning monarchs, and the British are reportedly considering the same.