No, it does not. Give me a source that confirms that Demon Hunters can turn into a demon type that don't even exist in game.
Since you ask so nicely, I will provide you with needed information.
Wowpedia said:
... As a demon hunter grows in power, they undergo a gradual evolution, becoming more and more demonic in appearance.
... The demon hunter’s gradual evolution achieves its pinnacle as they become a demonic entity. Their appearance has changed to something frightening: The exact changes vary, but can include glowing red eyes; horns; clawed feet and hands; nonfunctioning wings; cloven hooves; a spiked tail; dark skin; a deep, rumbling voice; and similar cosmetic changes. The demon hunter becomes an outsider.
... At the pinnacle of evolution, Demon hunters can unleash the demon in them and turn themselves (temporarily) into something more. This is called Metamorphosis.
Source:
http://wow.gamepedia.com/Demon_hunter
In WoW, Warlocks have this ability. Not Demon Hunters.
Really now? Let's take a look at some NPC from WoW. The NPCs below are fully trained Demon Hunters.
Alandien,
Netharel,
Theras,
Varedis (Note while Varedis does not have the ability listed, he does use metamorphosis as shown in
this video)
And of course the Illidan encounter in Black Citadel - he has his own phase where he is demon hunter.
Now the funny fact is: All these NPCs are add in patch 2.2.0, the warlock version of Metamorphosis is add in patch 3.0.2 as stated here:
http://wow.gamepedia.com/Metamorphosis
Kael'Thas originall skillset suits him well, the only spell I dislike is banish, it doesn't show that is an fire mage. Siphon Mana does not either but that is connected to the fact that he is a blood elf that hungers for mana.
Kael'Thas is not a fire mage but Blood Mage, which is something a bit different. High Elves favored water and frost spells, as fire spells were seen something similar to demons (brought only destruction and demons use (fel)fire and shadow spells).
However Blood Elves embraced this magic, so they started favoring fire and shadow spells. I think the general idea here was to show what a Blood elf mage is like - he uses fire spells, but also siphons mana because of their hunger and banish foes like demons (who they later use to siphon mana from).
All in all, wow should not dictate how a class should behave. For example Warden uses Blink (mage spell) and Vengeance (an incarnation of hate and all that bad stuff which could basically be associated with shadow magic). Yet they're good-natured melee fighters, so where does that leave them?
Wow had to make standards for the playable classes to differentiate one from the other, it does not mean the non-player characters should be limited the same way. For example Archmage Xylem uses Frost, Fire and Shadow magic (necromancy).