If bitcoins are becoming more and more popular and widely used in the world, then it is possible
Bitcoin is too unstable to become a country/state currency, meanwhile a country's currency also need to have some characteristics that bitcoin does not have for examples: It has to be stable, its value will be regulated and determined buy the government and the economic state of the country, all these features are not available in bitcoin which is why it will be far more impossible for it be a country/state currency.