Annealing actually softens the case. Allowing it to expand slightly and seal the chamber better.
.223 cases are usually annealed also, but are polished after annealing to produce a more appealing cosmetic finish. NATO specification requires visual proof of annealing which is why they are not polished.
It is not possible to anneal the "leade" which is a dimension and not a piece of material.
The part that makes up the leade dimension is longer. Look at th SAAMI drawings of a he cases.