I didn't know Ford was calling them resonator boxes...
by definition a resonator is an appliance for increasing sound or resonance so by definition if you remove it your exhaust should actually become quieter...
For instance, I have true resonators in my catback, if you put my exhaust up against a guy that just has straight pipe, my car will actually be louder, everyone thinks you can't get any louder than straight pipe, which is not true...