I saw a mod which introduced perks as a reward to players who beat the game as a pacifist. But, is this actually possible within the vanilla, or does this rely on other mods?

Yes, it's possible.

The game was designed for a No Human Death MQ completion as a possibility.

Main Quest can be beat with one NPC death, and that NPC is not a human. And, I don't even think you need to kill that one, but I have not done that route.

Most of the side/misc quests can be done peacefully, but some require violence or death, like the one where someone sends you out to hunt Legendary Animals.

Who is that one NPC? The game still doesn't seem ideal for it.

Can't tell you in General.

Sent a PM

It is possible to get a House victory as a technical pacifist - aside from having to

It's possible to complete all other MQ paths with exactly one kill at minimum.

It would be very hard to do though. Near impossible, even. Are there any mods which add non-lethal weaponry? Like a stun gun or something?

Assuming that I know who the one kill is, technically you can keep him alive.

No this person won't be alive after a year from exposure if you choose not to kill them right then and there. It'd be a slow and lonely death for this person and I see that as the more evil option.

It really depends on how strict your pacifist rules are. If you can believe you're still a pacifist even though you may have killed indirectly and not by your own hands or whatever weapon you're holding then yes New Vegas can be completed as a pacifist.

However if you feel killing somebody indirectly doesn't make you pacifist then no you can't complete New Vegas as one. Somebody be it a single person or a group is going to die or has to die during one of the four main quest-lines.

Yes it's possible to play through the game with just one death on your hands. I suggest you make your Charisma at 10, and get some followers, trust me, it'll make things so much easier.