yeah, nah. In a post-civilisation state where we're back to burning wood for heat, possibly.
But just at a basic level, he temperature control on the purification step must be so precise that it has to be electrical heating. Which means 'carbon intensive' isn't really the right word, they mean energy intensive.
Losing that wouldn't be "no computers" it would be close to "no electricity". Incandescent bulbs, resistive heaters, valves in your TV and radio. No internet, obviously