I do think it would happen but the only difference will be Countries would keep an eye on the address owner like coinbase does 
Any of the government provided facility does not gives you anonymity and it will never. And countries like USA and China will never give anonymity to their citizen. The same implies to India also, Gov will make several laws before allowing a user to use a gov run crypto currency.
Indian government will definitely make laws and there will be argument about it. Bitcoin system is working pretty well now and anonymity is one of the reason for its success. Many websites now accept donations in the form of bitcoins. If anonymity is lost, bitcoin users wont be happy. Any of the government provided facility does not gives you anonymity and it will never. And countries like USA and China will never give anonymity to their citizen. The same implies to India also, Gov will make several laws before allowing a user to use a gov run crypto currency.