Stupid question..
Worst of all, there is no relevance in the question.
Since we all know exactly what an arranger key is.
The fact if its an instrument or not?
doesnt change anything at all.

An Oboe is an Oboe, a piano is a piano, and an arranger key is first and foremost an arranger key
Under the hood its more like a chameleon
That on demand changes from organ into piano, into clavinet into synthesizer, into:any instrument with black and white keys
On top of that it allows you to emulate almost any other instrument you can think off..
And then you have a few ways to create a backing? Its like a guitarist or singer using a backing..



An arranger keyboard workstation is as it is..
And discussing if it is or is not an instrument does not add anything to what an arranger keyboard is.