Body enchantment magics must exist!
Anyway, I think it would matter how close the chorae got. If a flying chorae arrow made a glancing blow and was mostly defected by the fabric of the dress, then the which would stay afloat. If the arrow was nearly a direct hit and the folds of the dress mostly just prevented the chorae from touching skin, then the which would surely fall.
BTW, chorae are not pointed, just round balls of metal attached to an arrow. Since the chroae need to make direct skin contact, it seems improbably that any schoolperson would take the field in anything less thick padding. Close contact to the chrorae would knock you out, but even an inch of insolation would surely save your life (based on Akka getting slammed in the face by Ironsoul's closed first around a chorae, causing pain and minor salting) ( that happened right??).