Sure, in short:
The scola as an elite unit of the Carolingian military is mostly an Osprey-ism, as it was in an Osprey volume or a similar publication and now everyone believes it, perpetuating the idea it was an elite unit only.
It is not an entirely absurd idea. scolae could appear in a military context, but that is a gross simplification of what they were. They were indeed bodies for schooling and training young nobles in all necessary arts and sciences, including warfare. There were many different scolae, some probably had a stronger military focus than other, and it is not wrong likening them to an officers’ school or cadet academy. Indeed members of a royal scola, not the whole scola, could form a royal bodyguard. But scolaealso included people exempt from military service, monks. Unsurprisingly, the scola palatinae served as role model for Carolingian monastery schools.
Consequently, as far as the military use of these bodies is concerned, they were really seldom as such on the battlefield and all these instances (of which I am aware) were before TGC’s timeframe. Lastly, it must be not forgotten that the most famous example of a military unit called scola, the scola alae recorded by Notker in his Gesta Karoli, is evidently a simple transcription error.
Since we have ample evidence for elite cavalry organized in scarae, and since there were also scolae that were entirely nonmilitary, I chose to put an end to this Osprey-ism. Should I have missed contemporary texts clearly identifying scolae as tactical bodies in battle, I am of course eager to know about them!
In a sense, we have the scolae in anyway, for their members were usually called pueri.