Yes it can use bitcoin for a troubled economy. If the government accept the bitcoin it will help the economy for the country also for bitcoin it gave more money and it will increase the price.
It is a good opinion, however Bitcoin, or cryptocurrencies in general, are volatile and changes their value every time. Relying on digital currencies will be risky for an economy. I could only suggest that it could only be used and only co-exist with the fiat money.