In the event of the banks allowing Bitcoin fixed deposits means, the banks will have access to the transactions of individuals who have their Bitcoin with them. I don't know which will override the other if these bodies are to come together and work as one piece. Bitcoin is decentralized while the banks are centralized.
Bitcoin is decentralized , that's the main feature of it , banks are centralized because they need to control everything in their system not like Bitcoin was helped by the Blockchain system .
So i don't think bank will fit with Bitcoin in anyway.