Short answer: No;
Long answer: Possibly.
The reason is that, in order for BTC to be considered as the world central currency, it is essential and vital that all countries must accept it to be the main legal tender in transactions. In addition, almost all countries must be technological adapted when they implement BTC as the world currency since it requires the connection of the internet in order to have a stable transaction.
However, imagine that the world central currency has a cap of 21 million. This would result to an inflation of its price where people would purchase it at a high price in order to transact.
It might be possible in the future but for now, the chance is very slim. Bitcoin has been getting a lot of restrictions even if there's a lot of countries now who wants to get involve in bitcoin. But the fact that the government personally is not supporting it, then it would be hard for bitcoin to become a world central currency.
And being a currency with high volatility, i don't think it will serve as a world currency if the value is not fixed. Because as far as i know, its volatility will always be there and might only be reduced if the government start controlling it.