No, according to https://www.bbc.com/news/technology-57811959, only about 7% of the hashrate moved to Kazakhstan (probably about 1 GW), which (according to https://en.wikipedia.org/wiki/Energy_in_Kazakhstan#Electrici...) only has about 10 GW of total electrical generation (out of 20 GW capacity). Coal just isn't competitive for bitcoin mining unless you can get someone else to pay for it, even when the plant is already built, so Bitcoin miners are in no position to fund the expansion of Kazakhstan's coal-burning generation network.

The hashrate fell 53%, hitting bottom in July, didn't finish recovering until December, and still isn't consistently above its pre-prohibition peak, so "much of the drop in the hashrate" wasn't picked up by anybody.