No, anarcho communism cannot be applied, except for one big communist government owning and controlling everything.

If you "bought an island" or some other land, you agree that land can be owned as property. Also to earn that money, you need to work and sell your products and services, meaning you agree that your labor has market value.

Anarcho-communism is a totally self-conflicting ideology that cannot possibly be applied and achieve anything good.

See:
https://mises.org/library/death-wish-anarcho-communists