I have two doubts about what you are raising.
The first is whether one can effectively "appropriate" what are international waters and establish an artificial island and a system of government there. I doubt it, because if that were the case, many countries could expand their territories by doing the same.
The other is about the sustainability of creating an artificial island there. We would have to transport everything on a regular basis. Starting with drinking water.
I don't see it.
Pertaining to your first comment that is indeed permitted under UNCLOS if you are talking about international law. However, under international law the artificial island will not get territorial waters which are 12 nmi or an EEZ which is 200 nmi. Don't quote me on this but I believe these created island would only get 500m of protection from the baseline. That being said, international law does not have any real enforcement arm and the only thing that would matter would be recognition from other nations.
As far as drinking water is concerned, You could establish rain water collection systems on every roof which would likely be more than sufficient for personal consumption. However, I am guessing some level of desalination would also be needed for commercial interests. Additionally, it is very likely that a fresh water reservoir would begin to form under the island seen on one of China's artificial island in the South China Sea. Look at the source below.
https://www.scmp.com/news/china/science/article/3090761/freshwater-reservoir-found-one-beijings-artificial-islands-south