I had written a fairly long post about this matter before deciding against it, as I wasn’t happy with that I’d come up with. As it stands, this is actually an extremely complicated question. But I have finally managed to arrive at some sort of a conclusion.
Let’s take an extremely interesting case when it comes to demonhood and undeath - Mannoroth. In the alternate universe, we see Gul’Dan effectively raising Mannoroth’s body, consciousness and all, from the dead, before sending him off to fight us. Now, when the fight starts, Mannoroth is literally a skeleton. Undead in all but name. Yet, he isn’t. He’s a Demon, not and Undead, and the ritual Gul’Dan performs is seemingly not necromantic in nature. He’s raising a dead body, sure, but what he’s actually doing isn’t raising someone from the dead, but rather rebuilding a Demon by pulling them back from the Twisting Nether and giving them a body to inhabit.
In short, he’s rebuilding and summoning Mannoroth, not resurrecting or raising him.
Why is this? Well, it’s due to the simple fact that demons, as confirmed countless times, cannot actually die in the traditional sense of the word. Any demon slain outside of the Twisting Nether simply goes back there, and any Demon slain within it apparently ceases to exist, meaning that there is no “dead” state for Demons the same way there is for mortals. You simply either exist or you don’t.
The implications of this are clear: It might simply be impossible to both be undead and demonic at the same time. They cancel each other out! A Forsaken who ascended to demonhood would no longer be undead, he’d be tied to the Twisting Nether and effectively have resurrected himself as something entirely different. However, it’s also possible that the fact that a Forsaken is undead would leave him cut off from the Twisting Nether. We know there are methods to ascend to demonhood, but it’s entirely possible that undead in particular are incapable of becoming demons, the same way a Worgen can’t become undead, for example. Their ties to life-magic and nature are too strong to be severed by necromancy, rendering them immune to the powers of death. Although this is apparently only the case sometimes because… Worgen Death Knights…
Ultimately, it’s impossible to say for sure, because Blizzard has never addressed this, and the lore around who can ascend to what is extremely inconsistent. We’ve seen both a demon and an Undead ascend to become beings of Light, and we’ve seen beings infused with the void or necromantic powers become priests or Paladins, capable of using Light magic. We’ve seen Worgen be described as impossible to raise as Forsaken, yet we’ve seen Worgen Death Knights - perhaps the Lich King was so uniquely powerful that he could break through the barrier and sever their bond to life and nature, or perhaps it’s a massive plothole.
Now, could you become a Nathrezim? No. That’s not how ascensions work. Although material from the Shadowlands reveal trailer and lore revealed in Legion might suggest that the Nathrezim, the Shadowlands, death magic and the void all share a unique connection. I would assume we haven’t seen the last of them.