No, it doesn’t. It assumes we’re using it here. If we beam the power to Earth from space, it’s the same thing.
It's quite possible that with "infinite" energy we could do mass scale carbon capture to offset the increased temperatures by rolling back the greenhouse effect.
We use it in space too, we just send food and manufactured products down the elevator.
You aren't really trying in good faith to think this through are you? This idea is over half a century old. Not getting it by now is willful.
Even today we're recognizing that compute does not need to happen here.
When we're talking about creating powerplants equal to roughly 5% of the insolation of Earth, I think we're sci-fi enough to discuss orbital datacenters or Mars datacenters or Jupiter fusion candle datacenters.