tl;dr - When "Arp/Seq MIDI Out" is On the only MIDI Note On/Off messages sent are for my key presses, not the generated arp notes. When set to Off then *No* MIDI Note On/Off messages are sent. Confirmed via both a MIDI track in Ableton 10.1 and the standalone MIDI Monitor OS X app.
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Only the Note On/Off for my key presses were being sent rather than the notes generated by the arp. Here is what I found when enabling/disabling the setting in the Globals:
On (D#2-F#0 to select, then D0 for On) - As described above, only the MIDI Note messages for my keypresses are being sent.
Off (D#2-F#0 to select, then C0 for Off) - No MIDI Note On/Off messages being sent at all! Total silence.
Note (heh) that I verified the above behavior with both Ableon (10.1) and MIDI Monitor (OS X).
So, I then saw that with a unit serial of 01335 I needed to do a firmware upgrade. While none of the release notes for it described what I was seeing above I figured it was needed anyway, right? Well, since doing that I'm now seeing the same behavior but reversed: D0 now disables it resulting in no MIDI Note output and c0 enables it but when enabled I still only get the MIDI Note messages for my key presses instead of the notes generated by the arp.
I do have a ticket open with Moog's support but, while I wait, if anyone reading this has any ideas or pointers I'd really appreciate it.