I think towing a chassis back to base/tent with a cow isn't needed, and would just encompass more work. Why not just fix it on site? You can bring the parts TO it.
Depending on the carry capacity, you could just use it to move lots of items from base to base, etc.
I wouldn't use something like this to make a run to Gun Runners or anything.

I think the wood gasifier is an interesting idea, dunno how it would work in game. It'd be different, but easy enough to find fuel. The would already be difficult to get, so I don't see it being a problem that it's easy to gather fuel.
Of course I'd be okay it if was SEC/MFC/Rotgut powered, too.
Really the only thing that isn't "falloutish" is the color, which is easily changed, IMO. The concept is fine.