To me the definition of 'arranger' is some form of orchestrated auto-accompaniment. Usually with chord recognition that augments or complements the keys being played in real time. I wouldn't call the Roland DisCover 5M an arranger, nor Band in a Box software. But the tiny Yamaha QY-100 "walkstation" qualifies as an arranger IMO, because it has "patterns" (styles) and real-time chord recognition.

None of these are musical instruments by your definition, because they don't produce an original sound. Most Korgs and the Casio MZ-X500 have synth engines that allow a user to synthesize an original digital sound using layers and LFO's. They are true synths, that also happen to have a complete arranger feature set.

Some mechanical band organs from the early 20th century might be the first arrangers. They had paper music rolls, and some of them had keyboards for real-time play. These things definitely made their own sound, enough to fill a room!

So I guess what I'm saying is that being an "arranger" isn't sufficient to make something a musical instrument, but neither does it prevent something from being one.