@RNDM1 Just because people sailed and raided does not imply they practised agriculture.
I think you are drawing your distinctions a touch too cleverly. The Iroquois and Hurons in Northeastern Canada, say, were agriculturists--they had things that other agriculturists recognized as farms, they planted fields and such. The Amerinds of the Pacific Northwest did not. They managed the forest, sure--but it remained a forest, full of wild animals, with plant species basically as normal, just tweaked some in the direction of more useful food species. But that's true of almost everyone anyone calls a hunter-gatherer, and was probably true in much of the stone age as well; if you want to claim people who did that for agriculture, then you have to stop talking about the "development of agriculture" as a distinct phase in the first place. Then you have to invent a new word to mean what we normally mean by "agriculture" so you can start talking about the distinction again. So I don't think your way of doing the definition is useful.
I also think your discussion after saying "mode of subsistence doesn't matter that much" precisely describes a distinction in mode of subsistence. That is, you point to a group having better nutrition
precisely because their mode of subsistence is more mixed, with some agricultural base but much more reliance on fishing and access to a fecund wilderness, where they could, ahem, hunt and gather to supplement their diet. Secondarily, you're talking about places with more dispersed populations, considered "barbarians", that is basically places with less centralization, division of labour, and class distinction, pointing again to the distinction I draw where agriculturists would eat worse due to elite expropriation.
So, sure, I'll agree that not only did hunter-gatherers have better, more varied diets and less expropriation of the fruits of their labour than agriculturalists, but the
purer the agriculture, the less opportunity for mixed forms of subsistence, and the greater the development of agriculture-based division of labour and class structures, the
greater the effect would tend to be. This goes right down to relatively modern times--English peasants before the enclosure movements, with traditional access to commons both in the form of fields and wild lands where they would supplement their subsistence, were better nourished and more prosperous than English peasants after the common fields were enclosed and the common wild lands taken from them with new laws banning their use as "poaching". So much so indeed that many were forced to stop farming and go work in the cities for wages.