Dave Roberts has written a thought provoking blog post. My read of his piece is that he is telling a "Elvis Presley" story. Back before he was rich and famous, Elvis had a small carbon footprint because he couldn't afford several cars, a pool, lots of steak and a big house but as he got rich , he lived the American Dream and had a much larger carbon footprint. Roberts doesn't mention Elvis but this scale story is his story.
To an economist, consumption has a quantity and quality dimension. Roberts is fixated on just the former. Really poor people are more likely to burn coal for heating and cooking and poor nations will use coal to make power (because it is cheap). As poor nations grow richer, they move up the energy ladder in order to reduce their local air pollution exposure. Roberts piece abstracts from this point that richer people and nations consumer higher quality (and thus cleaner energy). California is rich enough to load up on renewables.
His piece also ignores endogenous technological change. We celebrate that the Tesla powered by solar panels will allow us to live our American Dream without the carbon emissions but would the Tesla exist if we were all poor? The key idea in the endogenous technological change literature is that there are large $ fixed costs to designing new products such as the Tesla; only if aggregate demand is high enough will for profit firms bear the risk to do the R&D to produce the product. Dave Roberts needs rich people to populate our economy and to vote their pocket book on the first generation of solar panels and Teslas. Mass production of these prototypes leads to competition and falling costs but the first movers here are the wealthy. He might counter that in the Manhattan Project that the government lead the Big Push.
So, if you combine the energy ladder point with the endogenous technological change point; your views on whether income growth is "good" for fighting climate change might change a little bit. Income growth also makes people more willing to vote for carbon tax policies because their pocket book concerns are lessened. Read my paper with Matt Kotchen on this point.
UPDATE: Perhaps a more interesting question here is; for a fixed income distribution (so 1/3 poor, 1/3 middle class, 1/3 rich); if you tax the rich and give the $ to the poor what happens to total GHG emitted. My hunch is that GHG emissions rise. Why? The poor have a higher marginal propensity to consume and they will now buy a old car (not a Prius). The rich would have saved that money that you took from them and would have used those savings to consume in the future. Since in the future, our GHG per $ of income will be lower; future consumption has a lower carbon footprint than current consumption (this claim is based on endogenous technological change).