Is it possible? Probably yes. It is all open source software, after all. Will it be trivial? Most likely not.
Applications can provide their own "open file" dialog, but more frequently call upon the common dialog provided by the toolbox that the application uses, e.g. GTK3 or QT5, to provide consistency between different applications that use the same toolkit. That is also what Chromium or Firefox do. Replacing these calls to the system dialogs with your custom dialog would require to "hack" the API of the specific toolkit such that a call to that dialog returns your custom dialog instead.