As it seems yes, but we are still far away until this comes true. It's not easy to ''make'' all people to use bitcoins. And it will be very difficult to make it a legal currency everywhere in this planet.
Exactly, to implent this all over the world is so difficult, it really takes time to make it as legal currency because as of now there were countries that banned it so for sure it will be hard to implement. But then the all we need is to make the government enlightened by the fact that bitcoin is a good way and source of income that makes people leave the financial problem.
But bitcoin must be the good example how people's consensus will be working. When more people of the world will be preferring one system, I guess government will be forced to change their stance. I'm sure it will be happening in future at least government will not be interfering into people's preferences. Moreover bitcoin system never need any help from any government nor central banks.
But I'm afraid people may take more time to use bitcoin as currency because right now they are treating bitcoin as store of value. Only when people will be ready to spend bitcoin for their daily life, we can think about bitcoin as a currency.