Sure. But they only have real power insofar as states agree to treat them as the ultimate authority. Which is very unlikely to be the case if they tried to implement such policies.
Consider that we have a UN-managed organization that handles mail and post on international level - Universal Postal Union. In fact, it's over 130 years old, predating UN itself. And yet no censorship resulted out of it, aside from what the countries themselves implement in their respective jurisdictions (which they can always do regardless, as sovereign states). Why? Same reason - if UPU were to get too heavy-handed, the drawbacks would outweigh the benefits of a single standardized mail exchange system, and large players would simply withdraw.