Yes you can. There's a dedicated button that puts it into "user" mode, at which point you can use it as a general midi input device. Every button and encoder is mapped, including aftertouch. You can program the LCD display and set the colors of the pads (via midi sysex messages).

I'm not sure how programmable the display is on the Push 2, as it's a different display tech. I imagine you send it snapshots of a framebuffer rendered on your computer.