I think we need clarification on what "via MIDI" means in this context as well as what the MIDI sequence looks like in the DAW.
The KSP supports one MIDI channel per track. If you play a sequence via the hardware MIDI in *and* it contains one or more of the MIDI channels that are assigned within the KSP it will funnel the incoming note stream based on the MIDI channel to each track while recording. Recently I did this to get some tracks from my old Beatstep Pro into the KSP. You need to do this a pattern at a time and the KSP needs to be set to receive transport control messages so it starts at the same time. You also need to manually set the bar lengths on each track to match what you are sending and it generally will need to loop a few times to get all the notes due to the MIDI delay at the start. It does work though, at least it did for me.
The key is that the KSP is pattern based so can at maximum have a bar pattern with 64 steps total. If you can make your DAW loop for each pattern, you have a max of 4 MIDI channels and you need no more than 16 patterns per track you can likely reconstruct sequences in the KSP. If you have a freeform sequence that does not use a pattern approach or it would require more than 16 patterns per project then you are out of luck.