Is it possible to make all text fields in OS X editable with Vi keybindings?
There is an OSX only way to do this, without using any 3rd party apps. You just have to create a file   ~/Library/KeyBindings/DefaultKeyBinding.dict and put what you want in it. See an example.

Since I dont use Vi, I'm not sure what the specific keybindings are, but there is a great page about Customizing the Cocoa Text System that should get you going.