Hi Suess,
As far as I know the rule of thumb is the main functionality (like budgeting for e.g.) should be fully up and running in the back end ERP system before even attempting to start implementing the corresponding Fiori app. As you have correctly mentioned Fiori just presents a much better UI than the traditional SAP GUI based screens to achieve the common SAP functions. But that does not mean that if some specific functionality is not present/activated in the back end ERP system then implementing the Fiori app will make that functionality work.
Regards,
Saurabh