here's how you do it. Open up your Privia. Find the speaker, follow it to the amp then cut the wires from the system to the amp. Now solder wires to the amp wires,solder those wires to a 1/4 inch audio jack, mount it in the case, reconnect the amp wires and the wires coming from the board/PCB. Congrats. You just modded your system.
Aside from that, no, you can't send audio through a midi cable. You really do need to learn how your tools work. Midi is a control protocol. Midi messages are 3 bytes. That's it. That's all. 24 on or off messages. If you did somehow turn midi into audio, it would sound very very lo fi and very harsh considering that it's 1s and 0s and therefore square waves. Even then, the device on the other end would need some kind of firmware modification or hardware modification that would require some awesome wizardry. I'm not sure it could even be done then, but for your purposes. No. It can not be done unless you plan on reverse engineering both devices, redesigning hardware, reverse engineering, reprogramming firmware, reflashing the system, and that's just the start.