I think btc to increase a country's GDP or change a country's economy may be difficult for now because the anonymous nature of BTC will make it difficult to calculate into a country's GDP, especially to measure the economic level of a country that requires a detailed calculation, the nature of BTC this anonymity also makes many governments make rules against BTC to avoid money laundering
Bitcoin is highly volatile and can not control by any one. Fiat and bitcoin and never live with each other. If you once use bitcoin you'll never use your fiat because its tax free and no one want to give any taxes.
Not stabilize but it has much power to improve the economy. Now days many people are jobless. They;re looking for jobs to support there family. Bitcoin opens some source where unemployed people can make money without doing highly invest.