The quick answer is I don't know. But I would guess not. The Yamaha DGX-650 is a sampled digital piano (IIUC) with some extra voices. The breath controller will be outputting a MIDI control change (CC). You would need some way to route these MIDI messages to an instrument with some kind of response to the CC.
If I think about the extra voices available on my Yamaha SH system, there is no way to connect a CC to, say, the volume of an organ voice to control, say, the swell by breath pressure.
On something with more of a synthesizer character, however, I imagine that I could route the breath controller's CC to whatever parameter the instrument made available - the volume of a flute or to the pitch bend of an oboe for example.
Then there's the question of making the MIDI messages available to the software from the USB socket. It seems the DGX-650's USB is just for memory sticks for reading and writing midi files or audio files. It doesn't look as though it has actual MIDI (DIN) sockets either.
I could be wrong though. There are a heck of a lot of buttons on the DGX-650.
Edited by de cajon (Today at12:10 PM) Edit Reason: Clarification
Hard to tell if this would work but you'd have to use the printer-style A USB port on the back of the DGX-650 to connect with anything you want to control or use as a control. Since that controller uses a B jack that's the first thing you have to figure out. As de cajon points out, it won't work in the B port on the front of the board. Judging from the specs, the thing looks like it wants to talk to a computer. But they also make one with a DIN plug for direct MIDI connections. The manual I found online doesn't say whether the DGX-650 has anything other than a USB A port on the back.
There's a MIDI reference document here that should tell you what the DGX-650 will or won't do.
With this model you don't need a converter between the Breath Controller and the DGX-650
Quoting the UNI MIDI Breath Controller manual:
The UNI MIDI Breath Controller is a Breath-to-MIDI converter for use with any MIDI device accepting CC data though a USB port or DIN connector. It has a built-in pressure sensor as input and generates continuous MIDI data corresponding to the amount of breath pressure applied to it. The MIDI Breath Controller can be programmed to send any CC on any MIDI channel. E.g.: • CC1 - Modulation wheel • CC2 - Breath control • CC7 - Volume • CC11 - Expression
I noticed that the orchestral samples inside the DGX-650 were from the Tyros. I used a similar setup on a Tyros and was not happy with it. I ended routing Amplitude to the modulation wheel within the Tyros. I got a better effect within the Tyros and ended up not using a breath controller. YMMV.
The UNI MIDI Breath Controller sends identical MIDI data on both cables (USB and DIN) but it is powered exclusively through the USB connector and has no internal battery. This means that when using the DIN connector only (for example standalone use with a keyboard/synthesizer), the device still needs to be powered through the USB connector. Power can be supplied by e.g. a universal USB charger, which is not included in the package.