I own a PX-560. The first option in the system settings is a toggle for the internal speakers ON/OFF. Independent of the status of the headphones or the external audio/line out ports. The USB does not carry audio. Just bi-directional MIDI.
It's a nice system but the newer Privias PX-S3000, etc also have speakers. They are much lighter which may be
important to some folks that must lug it around.
If it's stationary I recommend the hardwood stand with the 3 pedal arrangement to avoid that damn sliding pedal problem with the
MIDI sustain pedal. Using the 3 pedal hardware frees up the aux pedal port for an expression pedal for the organ sounds.