No digital 4-track I've ever seen can record MIDI. they can only sync to it, most of the time only as the master. This means that either a hardware or software sequencer could follow the 4-track, so that the audio tracks from the 4-track would play back in time with the MIDI information from the sequencer. You would then need either extra inputs on the 4-track's mixer to input the MIDI tracks (as audio, not MIDI) or you would need an external mixer.
You could record the drum info as audio, by playing back the software drum tracks and recording the sound card output into a track or 2 on the 4-track.
the other downside of "syncing" the sequence to the 4-track is that it takes one audio track for the timecode. So now you have only 3 audio tracks to sync with the sequence from the computer.