No, the economy will not become more stable.

Single currency in one country lose the independence of the exchange rate and monetary policy, the main cost, the single currency is the exchange rate and the loss of monetary policy independence, will greatly weaken the macroeconomic policy makers to cope with asymmetric shocks.

Neither the free flow of elements nor the centralized central finance are currently lacking among the countries of the world and cannot be owned. So if there is a genuine currency at present, the economy will undoubtedly become more unstable.