I don't have any experience with the DGX-660, but on my PSR-E and related models the Sound Control app does affect the "live" keyboard parts-- that is, the Main Voice and (if I remember correctly) Dual Voice. If I'm not mistaken, a lady who used to post here some years ago had one of the earlier DGX models (DGX-640, perhaps?), and she once mentioned using the Sound Control app to change voices during live play in the same manner that she could do with her since-sold PSR-E433(?) model.
Note that there are other apps from third parties which let you sequence MIDI messages to your DGX-660. One app that used to have a free "lite" version is MIDI Designer, which lets you design your own virtual controller on your iPad or other supported tablet-- that is, you can put together your own choice of buttons, sliders, knobs, and so on, arranging and sizing them as you wish, and programming each one to send a particular type of MIDI message-- Program Change, Bank Select, Volume, Pan, Reverb Depth, Filter Cutoff, Filter Resonance, Attack Time, Release Time, and so on (whatever your keyboard can respond to, as specified in its MIDI Implementation Chart).
However, in general the DGX, YPG, PSR-E, PSR-EW, and YPT models don't allow received MIDI data to affect their keyboard parts-- that is, the Main Voice, Dual Voice, and Split Voice. But what you can do is set their Local Control function to "off" so they don't generate any sounds in response to the keys you play on them; make sure their Keyboard Out function is enabled; connect a computer or tablet and send their MIDI messages to an app; and have the app turn around and send the MIDI messages back to the keyboard's MIDI IN. In effect, you will be using the keyboard as a MIDI keyboard controller to play the keyboard as a MIDI sound module. This seems like an awful round-about way to play the keyboard, but what it does is allow you to modify the MIDI data in such a way that you can make use of the keyboard's full MIDI capabilities, such as creating splits and layers that use all 16 MIDI channels, or editing the voice parameters in ways that aren't possible using the keyboard's own panel controls and function menu.