Is it possible to go through the game on very hard/hardcoe with your special all set to one an not picking any traits or gaining companions?

Right off hand, I'd say yes. I mean, as far as I can tell, without modding, it's impossible to even set your SPECIALs all to one and no pick a trait. So yeah, that would make it an impossible playthrough.

It's too bad I tried once too.

The sad part is that even if you could do that it wouldn't really make things all that much harder, since the AI is dumb as a post.