Yes, it's essentially a factor of cost, not electrical consumption per se. So at best I don't see it helping to reduce the carbon foot print. In fact, there is a chance the problem would get worse.

Consider the Braess Paradox as an analogy. https://en.wikipedia.org/wiki/Braess%27s_paradox It's possible that increased efficiency (more capacity) would incentivize a greater number people to mine until usage was higher than before - similar to how expanding roadways creates more traffic. Then again, there might not be the time for the problem to get worse before people realized that money is the bottom line, not conservation. Why bother with greener chips.. when it's faster chips that matter. That's one of the big problems with proof-of-work consensus. The game theoretics work against our survival interests.