Well, yes and no.
Small-scale agriculture is always local, but local doesn't guarantee non-industrial. As isolated as some people may be from agriculture, there are few places in the USA that aren't within 100 miles of industrial farms.
Buying local industrial-chemical food means I'm poisoning farmworkers whom I might meet, poisoning the aquifer that might feed my own water supply, and infesting my own neighbors and maybe myself with diseases. No thanks. (Not that I mean NIMBY, only that "local" poses no advantage and in fact is a personal disadvantage when agriculture is industrialized.) I'll choose long-distance organic over that. Even though organic standards were severely diluted at the urging of industrial agribusiness, they're not completely worthless.
Also, depending on your jurisdiction and the rules of the particular market, buying at a "farmers'" market doesn't always guarantee that produce is local. It burns me up to go to a "farmers'" market and find produce imported from hundreds or even thousands of miles away.

So, if produce comes from a small-scale local farm; if eggs, meat and cheeses are
truly pasture-raised; then yeah, absolutely, the "organic" label is a plus but absolutely not a requirement. But if you're buying some products of industrial agriculture (and face it, all of us except maybe GLC1968 do, and I don't think even she grows, threshes and mills her own grains), then the "organic" label is definitely an important value-added.