I'm doing something like this. My premise wasn't being a pacifist - I found that a bit unrealistic in this world - but I'm not using weapons at all, including not by proxy via companions. So it should be more or less the same as what you are saying, except I may have a slightly different attitude in some dialogs

E.g. if I can talk one guy into killing another for me then I would probably do that. I would just never shoot him myself or get a companion to shoot him (in fact I don't even get any companions, because I couldn't restrain them properly). I'm playing on hard btw., because it's my default difficulty, but note that avoiding combat makes the difficulty level meaningless, as it only affects damage taken by the player and by NPCs. hardcoe seems to make only a small difference as well, certainly less than on my other playthroughs (that are all on hardcoe).
I did rush the main quest a bit because it opens up more areas for questing, and I chose to work for the NCR. So far I've only encountered one quest where I almost had to shoot someone.
Spoiler
When dealing with the Omertas for the NCR, you'll inevitably end up in a room with Cachino, Big Sal and Nero and you will be attacked by Big Sal and Nero. You can get Cachino to fight Big Sal and Nero, and you can get Nero and Big Sal to fight each other, but the only way I found to resolve this without killing Nero (who is packing an assault rifle) myself was looting the key to the office from Big Sal as soon as possible and running away. The guards outside then eventually killed Nero, but not before he went through several of them.
I've not yet decided what I would do with quests where I can only avoid killing people with weapons by doing something else that also results in their death, for example
Spoiler I think killing everybody at Cottonwood Cove by dumping that toxic waste is almost out of the picture. Saving the slaves, knowing that the Legion will shoot them, seems to be out, too. But as far as I know, these aren't necessary to win the game, so I'd likely just ignore them.
I also killed Benny using the Black Widow perk. That can actually be avoided but I really like how the perk actually deserves its name in this game
I picked 1 strength btw. Don't need a lot of it if you don't have to carry weapons or ammo. You can make a lot of money by selling a small number of heavy items, for example
Spoiler
When I got to the strip, I stole the Plasma Caster from the Silver Rush shop. This is worth 4k caps alone. Stealing it is trivial because you can just leave without anyone bothering you even if you take the weapon while they can see you. Just don't steal more than one item in that way or they will attack.
Not needing all those fancy weapons and armor means I get a lot more free caps early on. On a non-pacifist playthrough I would almost never sell an expensive weapon, either it's good enough to use or it's useful to repair others with.
In total, my SPECIAL stats were at start:
Strength 1
Preception 1
Endurance 3
Charisma 9
Intelligence 9
Agility 8 (+1 from small frame trait)
Luck 9
Str 1 still lets me carry a weight of 160, as outlined above I think this is enough.
Perception 1 is a bit of a handicap for running away. At least in theory. In practice I found that it's good enough and it's actually better if I only see red dots for enemies that are near enough to actually be a danger. It can be easily boosted to 3 with items, but I'm not doing that so far.
Endurance 3 is what I had left from maxing the others, but I figured I don't need more than three because I really only want to implant charisma and intelligence - and that still leaves one.
Charisma and intelligence are obviously 9 so I can get them to 10 with implants. They affect my primary skills (speech, barter, science, and so on) and they make sense for a pacifist character.
Agility is high mostly for RP reasons (it doesn't affect running away as much as I'd like it to), but some points are necessary for perks like silent running. I took the small frame trait because one extra stat point is too good not to take, even though neither high agi nor higher chance to become a cripple change much in this game.
Luck is high for RP reasons too, but also affects all skills, so it's not useless. Could also balance some of the missing loot I'm not getting from people because I don't kill them, but it turns out I don't really have a cap shortage anyway.
I've been frapsing this playthrough, but I haven't yet posted most of it to youtube. So far I've only posted two excerpts:
http://www.youtube.com/watch?v=4olRMdijpec lifting the Bomber, because someone asked a question about this quest
http://www.youtube.com/watch?v=zOKuHw1eroo George getting himself blown up
As you can see my character is wearing a dress, armor doesn't seem to make a lot of sense if I'm not going to fight. Currently she's wearing a suit from one of the minor factions because I got tired of the dress. Either way, this negates two or three missing strength points just because I'm not wearing a 20+ weight piece of armor.
One thing I did early on was skip the entire early quest line and run to the strip as my first destination, where I "acquired" the chip. Then I continued with the NCR quest line. I've documented getting to the strip at level 1 here, but this is on a different character that I only made for this specific video: http://www.youtube.com/watch?v=NoueiV8ZRfk
Actually making that video is what gave me the idea to try a non-violent playthrough, but in that video I wasn't in the mindset yet as you can clearly see at the end when I meet Vulpes Inculta.