no, i don't think so, but i think it will "accompany" USD more like now, and it will become more and more popular
I also think so that bitcoin is not going to replace dollar , as dollar is one of the most stable and reference currency of the world, while bitcoin is comparatively newly generated currency therefore it is not so easy that bitcoin will replace USD so easily. But surely we can expect a big competition among these two.
I don't think that any competition even exists within these two. Bitcoin will continue to gain popularity among the users of Internet, and slowly, it is going to become the only currency which will be used "online", meaning no PayPal, no Payza and no stupid limitations. It is going to be a great asset for internet users, with very much freedom.