OK, one last time. NO, the FC7 will not work. It is an expression pedal and the DGX-660 does not even have a port for an expression pedal connection.
Picture one that I attached shows the back of the keyboard, there is:
Power cord connection
mic input
mic volume
aux in
headphones out
pedal unit (if you want to purchase their 3 pedal assembly)
SUSTAIN PEDAL
USB Connection
Contrast knob
NOTE: no expression pedal input for a pedal like the FC7 is available on the unit.
Picture #2 attached describes the sustain pedals that the unit accepts (that are Yamaha pedals):
FC3A (can do half-pedaling)
FC4 (can't do half-pedaling)
FC5 (can't do half-pedaling)
Other sustain pedals will also work, so you are not just limited to Yamaha sustain pedals, however the FC7 pedal is NOT a sustain pedal; and since the unit doesn't have a jack for expression/volume, the FC7 is not designed for your keyboard.