Nope. I very doubt government will want to relinquish control...
As a sub currency it could gain mainstream use but i think there will be much blood before BTC replace the Dollar.
Dollar has a very great influence in the global market really. Bitcoin on the other hand is unstable so most people and companies would prefer dollar. Let's just say that dollar and bitcoin has its own respective uses.
In real life uses, dollar or other fiats will be used dominantly especially in making transactions since what you pay is the actual price unlike Bitcoin which the price set to the deal would change its value at the time of the payment.
In digital world, bitcoin or other cryptocurrencies are suitable for transactions in this world since it is the most convenient thing to do. Also it is much suitable to use in paying services offered online.
Yeah we cannot deny the truth about the dollar that it is the most trusted and preferred currency in the world. When we compare the Bitcoin and the dollar we set aside the truth about the dollar that it is backed by the strongest economy of the world and it has the power of the USA on its back. The Bitcoin dont have any such facility for it to make it that much favourite that the worlds largest economies prefer it instead of the dollar.