can Cubase auto assign notes in a chord to a different midi channel?

Yes this is how to do it. I have four LE Presets - one sets the lowest note to Channel 4, another the 2nd lowest to Channel 3, etc. (see attached example). Put all 4 in a macro, assign to Key Command and you can easily split your parts into channels with a single key.

This works great if each chord contains 4 notes with similar lengths. But if you have a situation where all the notes change between chords except one note sustains so it is in multiple chords that can cause the LE to get a bit confused about counting from the bottom. When this happens it might require some hand cleanup afterwords.

Setting the Key Editor to color notes based on Channel rather than the default Velocity is helpful when doing this. Also the LE counts position from the bottom up starting with 0 for the lowest note, 1 for 2nd lowest, etc.