Evidence leans towards “no”. They specifically said when they added the class that the reason is only had two specs wasn’t because of limitations on design time or anything, but because they couldn’t think of a way of adding a third spec, whether DPS or tank, without watering down one or both of the existing specs.
As an example, one of the more common suggestions I see is to split Havoc into two specs, one based on the traditional Demonic build (ie. Eye Beam, Demon’s Bite usage, the Demonic effect being innate, etc), and the other based on Demon Blades, with or without Momentum included innately. The latter specialization would likely have to steal skills from Havoc to differentiate the two. Perhaps the Demonic sepecialization would only have one charge of Fel Rush, and lack Blade Dance (since they have Eye Beam for AoE). The Demon Blades specialization would likely lack Eye Beam (though perhaps they’d have Fel Barrage or Fury of the Illidari in its place, plus Blade Dance). And perhaps it would lack Metamorphosis entirely, instead using Chaos Blades or Nemesis as its primary DPS cooldown. It would likely have Demon Blades as the hardcoded default with no Demon’s Bite option.
Net effect is that each spec is roughly half of what Havoc is now. And if that’s how we get a third spec, what on earth have we gained by it? Specs are no easier to balance against each other than builds within a spec, so it’s not like it would change the probability that both playstyles would be viable concurrently (which, btw, they are already phenomenally close in balance, Demonic just wins in current content because of the AoE focus of Uldir and because of how astoundingly frustrating Momentum is to use in anything more complex than a Patchwerk sim). All we’d have is two specs that are both roughly half as dynamic and well-rounded as Havoc.
Now, all of that said, a ranged specialization has the most chance of success from that perspective, because it would require the last theft from Havoc, and would innately be differentiated substantially simply due to the ranged part. The reason that never made much headway, I suspect, is because the lore simply doesn’t fit it. DHs throughout the Warcraft games have always been high-intensity in-your-face melee scrappers, so having them sit at range would feel…odd for the class’s overall fantasy.
The two most common suggestions I’ve seen for that ranged specialization are two make one based on Wardens, using thrown glaives attacks, and a shadow-type caster using demon-inspired spells and abilities from range. The former is a significant stretch, since the Wardens and DHs have classically been somewhere in the ballpark of mortal enemies, so postulating that some faction of DHs was willing to learn their techniques, and some faction of Wardens was willing to teach them rather than throwing them in jail to rot, is reeeeeally hard to sustain.
On the other side, while a demonic caster spec makes a little more sense from the perspective of the lore background of the DH class (after all, we get like a third of our abilities by yoinking them off a demon we just murdered during the starting area), it’s a massive divergence from how DHs have been portrayed and characterized in the whole of Warcraft history. Such a caster would also require a different weapon setup. The Warden style could at least continue using glaives, either individually or in pairs (and would probably even use Agility similar to a hunter), but a caster setup would require intellect weapons and gear, meaning either they would no longer use warglaives (and then are they really a DH?), Blizzard would have to add warglaives with intellect on them (exacerbating the issue that warglaives themselves caused, since they are already a weapon only used by 1/12th of the classes), or all warglaives would have to have both agility and intellect on them, which would also be odd, though at least somewhat manageable. So ultimately, such a caster setup is also quite unlikely.
TL;DR: a third spec is quite unlikely, because there’s no real way to add it without diluting Havoc or trampling all over the established DH lore and characterization. And Blizzard said exactly that during a the lead-up to Legion, that they were only adding 2 specs because they couldn’t find a way of adding a 3rd without retconning DHs hardcore or making one of the other two specs substantially less awesome than it was.
