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.
It is true that bitcoin will not replace Dollar but it can bit the Dollar, As bitcoin market value is more and more than Dollar and its is onee kind of currency so it can bit Dollar.
What bit means? or you are referring to "beat" ? If ever what are you implying to. But bitcoin will not replace dollar easily, I'm not sure
if it can really replace it since it is a very stable currency of USA and as well as other countries are adopting dollar.