As in, a Florges with Flower Veil in a double battle beside a Rotom-M (y'know, the lawn mower!) and the Rotom-M uses Leaf Storm, would his special attack drop?
Flower Veil prevents the Pokémon with this Ability (if it is Grass-type) and its Grass-type allies from having their stats lowered. Self-inflicted stat reductions, such as from Leaf Storm or Weak Armour, are not prevented. -Bulbapedia
So to answer your question, no, it will not.