No, because governments simply won't allow this.
I also believe this is the main reason, Bitcoin is decentralized, they won't be able to control it.
The purpose why government is created is to control us through their regulation, fiat will always remain as the money in this world regardless of how much improvement in technology we will enjoy. Let's remain realistic and even bitcoin soar nothing will change, so let's enjoy bitcoin as an investment as well to take advantage when it moons.
If it does replace fiat I also believe it'd have to be under the provision of the government... and here's a crazy thought, no one knows who actually created Bitcoin, so it's
possible to consider that it was created by the government. I'm not saying this is the case, it'd be a very elaborate conspiracy... but they have sooooo much money at their disposal and recruit the greatest minds that it's certainly possible. I also don't doubt that as technology advances that ways will be found to manipulate and hack the system, like anything else.