In the Book 3 Finale, Korra was administered a deadly poison that was meant to forcibly induce the Avatar state. Unalaq being the Dark Avatar and the polar opposite to Korra and sharing a kind of spiritual link to Raava through Vaatu, would his body have reacted the same way?
This depends on why the Avatar enters the Avatar state. Is it an automatic reaction of the human, or an automatic reaction of Raava, or is it Raava's choice? (Aang entered the Avatar State before learning to do so to save his life in ice, and Korra entered the Avatar State while desperately trying not to do so; we can assume the human is not willingly entering the Avatar State when near-death.)
If it is an automatic reaction of the human, then we can assume Unalaq would automatically enter his Dark Avatar state. If it is an automatic reaction from Raava, then we can likewise assume Vaatu would have a similar automatic reaction.
But if Raava is actually trying to keep the human Avatar alive, then we would have to say Vaatu cares enough about his current 'partner' to try and save him. Vaatu may well have let Unalaq die in the hopes that his next incarnation would be stronger, or that the next one would be hidden and rise to power in the background.
All of that being said, Raava would not willingly break the Avatar cycle. If Raava could stop the Avatar State from happening when the Avatar is about to die, we would assume Raava would do so.
While it is never clearly defined, this reasoning makes it a fair assumption that the Avatar state is entered automatically by either Raava or the human, so Vaatu would not have a choice in the matter and Unalaq would therefore automatically enter his equivalent Avatar State when close to death.
There's obviously no way to be sure, but it seems safe to assume that Unalaq would similarly go into his Avatar State-equivalent when under threat. It's kind of a common-sense reaction: "if you're about to die, pull out your biggest guns."
I don't think there was anything special about that poison, it was just a way of putting her in enough danger to bring out the Avatar State, while also weakening her even while she was in it. It would seem that most poisons would have roughly the same effect.
So yeah, my guess is that if similarly poisoned (or faced with any dire threat), Unalaq's Vaatu spirit would have reacted to defend him, just like Korra's Raava spirit defended her.