High Speech, Barter, Sneak and maybe Medicine and Lockpick will easily get you through the entire game without using a weapon once.

If you intend to actually fight your way through the game, you'll have a hard time with just Boxing Gloves and a BB Gun. Good luck with Lanius and Ulysses.

you obviously never played this game with a pure melee/unarmed build haven't you? nor realized that in every conflict your in, NCR troopers are right behind you doing most of the damage, where you can just sit there and wait for them to kill the rest. Once you get through, you need only to eat healing food and stimpaks, along with slasher/med-x for a 50DR, thus you become pretty much immortal, walking all the way to Lanius, talking him down then boom, done. He's also not doing the DLC's.
a combo of
-Gecko Steak
-Gecko Kebab
-Bloatfly Slider
-Stimpak
-Grilled Mantis
-Caravan Lunch
-and if needed, Super Stimpak

this combo itself will nullify ANY damage ANY NPC can throw at you, period. with a decent DT threshold, you can basically walk in there naked and talk Lanius down while wearing a pair of golden gloves, along with a BB gun on your back.
If doing a House ending, it's even better. Securitrons with their explosive missile launchers and grenades make it a cakewalk :/

You could. Actually, speech is the most important skill, hands down, no one can argue. Speech is used the most and makes the game easier.

Cheers

Completion should be a piece of piss. Just don't hang about doing every second quest.

I have, actually. I've done two melee-only playthroughs. I used Knock-Knock, which made the whole thing pretty easy.
I don't really understand what you mean though, are you responding to the part where I said it would be hard to fight your way through the game with only Boxing Gloves and a BB Gun? That's true, isn't it? There are a lot of places where you don't have any backup, and only using these two items will just get you killed.

For example; trying to kill Caesar in the Fort, finishing the We Are Legion quest, taking the Fiend bounties for NCR (except for Driver Nephi), taking out Motor-Running for Hsu.

There are lots of fights hou have to fight alone. Most of these can be avoided by other skills like Speech or Sneak, but I was talking about the OP wanting to fight his way through.

Also you shoudn't make assumptions so quickly.

not true at all. Period. Why? Why do you think it's not hard? one answer, that all Unarmed/Melee Builders love the most: Survival. That skill alone makes stimpaks look like an idiotic toy and useless in combat situations, yet a dish of Gecko Steak, Kebab, Healing Power, Grilled Mantis, and Caravan Lunchbox is enabled you to become literally immortal. Hell, you don't even need the Caravan Lunchbox, just use one crappy stimpack with that concotion and all of that stacks up and stays there for 30 seconds or so (even better with Turbo, a must-have for Melee/Unarmed users). So yes, don't tell me a situation that's 'super hard' when I myself played throughout most of the game my first time with my bare hands and literally LOL'D at the things I could do.

side note: why kill Caesar? House doesn't want you to, and that's the easiest way to get a Mohave Victory in this game. All he's doing is going from point A to point B with just those equipment and beat the game, not survive in a DID playthrough (though it's still possible). Derp. Did you seriously just said the FIENDS are a threat?...REALLY? lol. With Toughness x2 and the Sub-Dermal Implant, a DT of 10 makes most of their weaponry useless (most? I meant to say all except Plasma Rifle, but their's is always in terrible condition so...yes, all of their weapons become useless against you.) Face it, the game is easier then you think.

Motor Runner is a joke. Unless you 'herp a derp' all the way in (which, again, is stupid) instead of just wearing a Great Khan outfit, do the Aba-Daba Honeymoon and do a sneak critical on him, wipe him out, and GG. Cook-Cook isn't a threat because with you are truly a unarmed person, You would've gotten Super Slam by now, and Slasher. Along with every other critical enhancer, thus giving you a high chance in knocking them any being or creature out in just a few hits (which they stay there for 30 seconds, enough time to continue beating them down, forever.)

Finally, do you know what you said?...Abilene BB gun does more damage in a Sneak Critical then Ratslayer, I mean seriously, the weapon alone can pretty much snipe most of the NPC's (Fiends especially) from afar with BB ammo. Silentpreacher just needs to do a high critical/Unarmed/Melee character, and he's got the game in the bag.

Okay, you have a point there. I suppose what you're saying is right, you can go totally out of your way with perks and inplants and finish the game with lousy weapons if you'd want that. I wouldn't know, I usually use rifles or axes/katana.