I doubt it

I doubt whether gut microbiome can produce health or illness as claimed 
(rather I think it's merely an indicator of health, an effect rather than cause)

We are auto-enzyme digesters, not ruminants. Unlike our primate "cousins" we've lost most of the large intestine mass and cannot ferment cellulose for a substantial portion of our diet no matter what kind of bacteria we contain.

Even if the human gut microbiome does have the power to produce health or illness, I also doubt whether you can get much benefit from implanting someone else's poop - if your gut isn't supportive of the appropriate bacteria implanting a small number of them won't make it suddenly hospitable for them

Rather than use the waste of hunter-gatherers as food, we should probably copy their food
(since they don't eat their own shit, it's unlikely that us doing so will give us a health result similar to theirs)