I do not think there is a way of distinguishing between "vat-produced" counterpoint and arpeggiated accompaniment, unless said accompaniment repeats the arpeggiated chord as an exact same sequence of notes every bar/division of a bar, whether it be by ear or on paper. Even then, counterpoint can be repetitive as well. There's too much to say here, as different musical genres employ different techniques: one might almost always have 1 chord per bar in some (for example, blues), and one might have many chord changes within the same bar in others (for example, progressive rock/metal).
If you take a look at some of Bach's fugues, you will notice that they contain repetitions as well. In other words, counterpoint can be repetitive as well. Polytonality doesn't imply variation necessarily.
That being said, I personally (and I am no expert: I am just a musician who doesn't have a degree in music or music theory) see this as a question about squares and rectangles. All squares are rectangles, but not all rectangles are squares.
Arpeggiated chords are one of the ways for constructing counterpoint. You can split a chord into different voices, remove some of the notes and construct counterpoint therefrom. Similarly, you can create counterpoint and build chords on top of that. Which method is taken depends largely on the composer, and I do not think it is possible to know for sure unless the composer clearly states how they have constructed the work in question.
Perhaps, the only cases where arpeggiated chord use is obvious, are when notes "go out of scale". Classical counterpoint usually has no accidentals (unless it's a piece in melodic minor or a trill/grace note). If there is a chord accompaniment going on, a chord can be borrowed from a parallel or relative key, and that's where chord-based composition kind of becomes apparent. However, even older classical pieces can employ this technique for constructing counterpoint. So the divide between the two is really muddy.
I guess, it's just important to know what genre you're dealing with and what era it comes from. Older classical music will be based on the idea of polytonality and counterpoint, whereas jazz and genres derived from it (rock, blues, metal and such) will have chord-based progressions most of the time.
I hope this sheds some light on your problem.