Both of these things are true, depending on what is meant by our range of habitat. A small number of people can survive just about anywhere just as you describe, but current population densities are not sustainable in many places without cheap abundant energy.

(I’m not actually concerned with us running out of cheap abundant energy; PV is already fantastic in this regard, and in a hypothetical collapse of all dispatchable power sources that included never being able to make more batteries, we would be severely inconvenienced rather than utterly finished).