I do not think so, and I will hope it will never happen. you are talking about digital currency, which means connecting to internet, local BANK also have it, such as e-banking, m-banking, credit card, and most of all is having physical (metal and paper) that can be used even though internet and the electricity is off. Then how can digital currency replace it? I would prefer if the digital currency and fiat will go side by side.
There is no doubt in this that some people are still unaware of digital currencies and they are quite reluctant to work with these currencies because according to them all these are spam but on the other hand, majority of people in developed countries are in favor of working with bitcoin and other digital currencies just because they know their worth. In short, in such countries digital currencies can replace fiat.