At the start of "Into the Expanse" you can end up as the only conscious person in a room filled with rival rouge traders. Anyone object to calling insta-gib due to a bolt round in the head from point blank range against a helpless target?

Aside from the fact that it'll be obvious who did it, I believe that it's understood that there are guards in the service of the witches in the room, and they wouldn't be affected. Also, the witches would likely take offense and either prevent you from succeeding and/or smite you for the attempt.

If you, as a GM are concerned that your players might try something like that, insert a disarmament scene - no bearing weapons into the presence of the witches when they're doing a foretelling.

Or, since one or more of the PC RT's group resisted being drawn into the vision, it's perfectly reasonable to think that some members of the NPC RT's groups weren't drawn in either, and are conscious to notice and/or intervene.

Hell, they are crazy rogue psyker/heretics. Who knows if just being near them will foul your weapon's machine spirit? And we all know that Rogue Traders rarely carry "cheap" weapons. I think, even without a disarming scene, they just need to be taught the ways people of their standing behave. You don't usually kill another Rogue Trader in the presence of witnesses, and even Winterscale needs support of the other Rogue Traders, in the Expanse, so if they are known for "not playing nice", they'll come to learn how hard it is to do business with anyone who also does business with their rivals. Even some of the belligerent RTs don't just off the competition, especially if it might cost them more, and then their rivals find them weakened, and vulnerable. It's a massive, byzantine web of relations, alliances, contracts, and vendettas, and how you play it will set you up, or tear you down, in that world.

In an abstract sense yes, firing a bolt round at an unconscious, unarmoured person would be an instant kill. Although they might have a force field in place that wouldn't be affected just by being unconscious.

Apart from the reasons other people have given you as to why it wouldn't work I'll throw in now you have the ships and crew of many dead Rogue Traders who seek you out for revenge, and in the hope that killing you gets them in good with the NEXT Rogue Trader.

Also, your rivals should have Fate Points, which means the GM can burn one to have them survive an encounter. They could come back with the Rite of Setesh, or through a daemon pact, or through your gun just jamming. If players object great, that means I don't have to respect their wishes next time they drop to a death threshold and just kill them off!

That situation was just an example. What I am really asking is when is it appropriate to ignore damage rolls and say that if you hit them you kill them.

I do it with mooks all the time, and never with plot characters.

That situation was just an example. What I am really asking is when is it appropriate to ignore damage rolls and say that if you hit them you kill them.

This is up to your own good judgement but the main part is that it shouldn't be without them being able to avoid or fight through it in some way (Though this can very well be very hard if you feel it should be. The issue of difficulty is another one). I'll give a few examples where I have used "death without damage" against players.

-A player was attempted to be assassinated by a Venumon assassin (he wore a Halo-artefact in the presence of an Inquisitor for those interested in the background). Instead of rolling damage for anything the challenge was in hard toughness tests and attempts to get him to a medbay quickly enough. He survived it but had he not I would still not have caused him a single wound before his death.

-Two players go into a suicide charge. I warn them twice that it is just that. With a good command roll it works at first and I give them a last chance to retreat back to their battlelines, warning them twice that they are facing certain death otherwise. They decide to sacrifice themselves for the dynasty and both are killed without bogging the moment down with fighting out the actual combat.

-A character has acted in a way that the rest of the dynasty just can't accept despite numerous warnings. The rest of the group throw him into a voidlock and when it's activated he dies.

-The grand-finale of my Only War campaign had the Deathkorps (now Company Command hated by the Yu'vath...it was set in the Angevin Crusade) acting as bait to attract several Yu'vath to one world for an exterminatus. In the final moments each player dies as they are overun by enemies (each given a moment to explain their last defiant actions) as the ship carrying the vortextorpedoes (the firing systems where jammed) is drawing near to crash and grant all of them a martyrdom to be envied for centuries on Krieg. Best. Partywipe. Ever.

-A player asks nicely to change character and I come up with a fitting end for the former which we play to before the switch is made.

Ah, see, now when to do instant death is a more general discussion. When you want generalities ... don't ask something so specific without making clear that it's just an example, otherwise that just confuses that issue.

The more general discussion of instant kills has happened before a few times, but the last few times I've seen that question I've also linked back to a previous discussion on the matter:

https://community.fantasyflightgames.com/topic/194775-do-you-allow-insta-kills-in-some-instances/

The caveat being that while it's technically an Only War discussion, it applies more or less equally across all the game lines.