I'm going to rephrase your request since "trigger" has a meaning apart from sending note on/off messages.

"Is it possible for the assignable switch 1 or 2 to initiate a note-on event in a certain PART?"

Not really. The only things that can initiate note-on events are your fingers playing the keys directly, an external MIDI message from another device, or ARPs. Motion sequences cannot even be made to initiate note on/off events. Only ARPs, direct keyboard control, or note on/off messages from an external controller/device (such as another keyboard or your DAW or ...).

Indirectly, you could make it "seem" that pressing [ASSIGN 1] or [ASSIGN 2] caused a note to start playing. I believe there are a few options, but do not have the keyboard setup to test.

One of the options I know will work is to volume mask a note. The other option I have in my head is less convoluted - but I'm not sure if ARPs respect articulation control.

So the convoluted way that I know would work would be to have ARP play a note over and over. The ARP should start (trigger) when you press any keyboard key and play, in tempo, over and over, the same note in the PART you want to indirectly cause a note event to sound. The default volume for the PART should be zero. The assignable switch should be momentary. Setup destination of volume with the assignable switch you want to use as a source. Set the switch OFF value (input=0) in the curve as an output of 0. Set the switch ON value (input=127) as an output of the volume you want for the sounding note.

Then you would hold the assignable switch down while you want to hear the PART's note sound.

I have a variety of other ideas but will just offer something I know will work (do something in the ballpark) off the cuff.