Answer: That is an interesting subject, and I can see why you'd think of arguing that way.

You may recall that there is a common figure in original classical sources in which you see a figure that looks like a grace note a second above an eighth. In modern editions this is sometimes just written out as 2 sixteenths, because the intent was for that grace note to be on the beat and given about half the value of the 8th. Why, then, did the composer write it as a grace? Because it wasn't part of the harmony. The 8th note was the chord tone, and this is still the period in which someone playing accompaniment would want to see at a glance the harmonies of the other parts. So a grace of that type could be called an nct.

C.P.E. Bach's Essay on the True Art of Playing Keyboard Instruments is a good source for information on early classical ornament. In the Norton edition of Mitchell's translation you'll find on p. 93 some illustrations of "appoggiaturas" as notated and as performed. Notated, Bach writes them as graces. Performed, they are typically on the beat, taking part of the time of the following note. They are, depending on approach, what we'd call accented passing tones, or appoggiaturas, or accented neighboring tones, etc.

Bach said, speaking of such graces played at the time of the following note: "Appoggiaturas modify chords which would be too simple without them... Appoggiaturas are sometimes written in large notation and given a specified length in a bar. At other times they appear in small notation, and the large notes before which they stand retain their length visually although in performance they always lose some of it to the ornament." "...Because of their variability, such appoggiaturas have been notated of late in their real length. Prior to this all were written as eighths."

Looking at it another way: is there any kind of decoration that does not involve use of one or more non-chord tones? The symbol for the turn can be interpreted in several ways, but basically it begins on the note above the chord tone, then moves through the chord tone and returns via a lowering neighbor tone. The trill and mordent are essentially extended upper or lower neighbor tones. These are all graces, and they overlap with the meaning of the various ncts used in counterpoint.

So yes, the purpose of these graces is to add complexity, style - grace. But they can be analyzed as non-chord tones; they are decorations of the chord tone - much as the standard counterpoint ncts of neighbor tone, passing tone, suspension, appoggiatura, etc. are written-out decorations.