For the Korg NTS-1, I am outputting something other than just note on/off events. The NTS-1 is somewhat unique that its arpeggiator computes arpeggio notes and timing onboard with three parameters: root note (the key you press), the chord pattern (major, minor, dim, sus, aug), and the arp pattern(up, down, up-down, random, etc.) and then generates the arpeggio. The root note is a simple note on, but the chord pattern and arp pattern are controlled through MIDI control change settings.

And the first question - also yes. But for synths other than the NTS-1 you'd have to send each note individually so you will more to do - e.g. keep track of note positions, determine notes in each chord, etc. I might try to do this too. As far as I know, the NTS-1 is the only one that has such a smart arpeggiator (probably because its monophonic and you can't enter chords easily...).