Will bitcoin exist with the current financial system? Or will it become a parallel system that coexists like two countries exist side by side? I believe it will be a parallel system? The fiat money will flow from traditional to bitcoin system slowly but surely. We are already seeing some indication of that happening. Around, $7Billions, have already poured into it. It is here because it no longer 100% believes in the USD or any other currency it holds.
You seem to make a differentiation between your two options when I do not find any, bitcoin since the moment it was created it has been coexisting with the current system so by definition it is also parallel to the current system itself, and since governments cannot get rid of bitcoin this is going to be true for the foreseeable future and since it is quite unlikely bitcoin will get rid of the current economic system then this is a status quo that will continue for a long time.
However as time passes bitcoin will grow in size simply because it is better than the system currently in place and as people realize the lie they have been told about the current system and how those at the top get profits unfairly out of them then more people will begin to use bitcoin as a way to protect themselves from that predatory system.