I doubt it.
Cryptocurrencies have great potential to replace fiat in day to day transactions, but even at that it would be hard to phase out fiat completely.
There'll still be a section of society that does things the old fashioned way. Better technologies don't always succeed in making the older one non-existent.
Take media for example; newspapers have bee around as far back as the 19th century. This is 2018, and despite the arrival of radios, television and the internet, there are many people out there who prefer reading their news in print.
The discovery of fire was integral in moving human civilization to where it is today. Despite that, tribes have been found in modern times that put their food in tress to warm them because they hadn't discovered fire yet.
Cryptocurrency will change a lot of things, but fiat will still be around in the near future.