Not necessarily- a poor country with high biodiversity or other natural resources are a known phenomenon [0]. Also, another known issue is that the most polluted rivers are often from developing countries, partially because developed countries are sending their trash there.
Resource curse is an interesting phenomenon, but I think biodiversity (~ the healthiness/robustness of the remaining natural environment) and e.g. the amount of accessible oil/gas a country has are fundamentally different aspects.
