Necrotic spells can have chance to apply damned, which is an ailment that applies necrotic damage over time, basically necrotic version of bleed/poison/ignite. There are various ways to get chance to apply this ailment in the passive trees and various skill specialization trees.
For the Death Knight node in Skelatal Mages, yes it looks like it just makes them deal melee necrotic damage, with the option to make them also deal melee fire damage with the Flaming Attacks node and can cast Hungering Souls with Death Blossom. Essentially, they become melee and they will scale with minion melee damage instead of minion spell damgae. Without looking into guides or the passive tree, I assume this would let you use Skeletal Mage specialization alongside Summon Skeleton and only have to worry about scaling minion melee damage. Normally Skeletal Mages scale off of minion spell damage.
The necromancer tree only provides flat damage bonuses to three types of damage: physical, necrotic, and fire. A lot of minions have direct interactions with necrotic damage:
Mages can scale with Profane Oblation and Wraiths can get 20 flat necrotic damage in the tree. Infernal Shade adds a flat necrotic damage bonus as well as providing a 100% chance to apply Damned.