> Does that mean the 'buy locally' idea has little climate impact?

No, buy locally has a large climate impact - only not in the direction you think. Local uses much more energy than non-local.

Local has no environmental benefits whatsoever - only negatives.

The only thing it has going for it is some nebulous social benefits of knowing your farmer.

I avoid local because it means the produce was grown not in the climate where it grows best, but rather forced (i.e. lots of extra resources) to grow near me.