Will bitcoin exist with the current financial system?
What do you mean by that? Bitcoin was created, has been used and will exist because the current financial system is broken. Bitcoin is an attempt to create a completely independent financial system, a system that governments cannot control. Although they can fight it and try to regulate it. For such financial system to succeed and replace the current one, it first needs to survive in battle with the states and central banks. They should be deprived of the ability and power of control money supply and money issuance. It is not going to happen any time soon, but still bitcoin nowadays can and should be used by people completely isolated from financial system, it is for them, after all, bitcoin was born.
I am lucky in a way because my country does not have an issue with bitcoin. Sometimes my country's indifference bear good results. Hopefully when the time comes, they will support bitcoin's existence. Regarding the question whether will it co-exist, there will be varying answers. Although the current financial system is broken and cracks are showing everywhere, the roots that it planted in nations are so deep that the system can't be rid of entirely. A coexistence will be of benefit for bitcoin but that alsl means the system it swore to replace will still live and the masses will suffer.