Not necessarily. Or rather, the growth of wealth could double every few months.

And this wealth effect could be due to massive reductions in labor costs by employing AI, leading to increases in standard of living as the price of good plummets.

I haven't looked at charts for the economy as a whole, but I bet certain kinds of technology provide nonlinear benefits for linear growth in energy consumption. Think about one computer replacing a roomful of workers doing hand calculations. (We don't moan about losing those jobs, by the way.) Yes, the computer was the results of decades of progress and investment, but looking at the marginal energy consumption of the finished good compared with that of a roomful of humans, there is no comparison.

Also, as long as we're talking sci-fi, why stop at harvesting energy from the earth. Until we capture 100% of the energy emanating from the sun, we have a long way to go as a race as far as energy consumption limitations.