I would answer it depends on the purpose of 'normativity' as you put it.
If subjects are 'normatted' (which has a good dystopian feel as a mix of normalized/formatted :-) ) in order to conform to a purpose, an intrumentalization can very well follow.
I can see such a process and result in education where students are tested/selected in order to conform to the available functions rather than grown and developed in order to further their own individual abilities.
I don't know for sure whether all 'normativity' entails instrumentality. So far, even though I did not think long about it yet, I can't see any 'normativity' that does not seek instrumentalization.
But I believe that 'normativity' is always setting-up limitations and is a sign of lacking trust and vision in the wide and diverse human possibilities. It reflects more than anything else the limitations of the 'normatter'.