AI would likely be a first-class participant or citizen in any early human colony in space. Our perception of risk-to-civilization changes significantly for off-world events. Just like the plan to build nuclear reactors on the Moon, the threat from AI isn't deemed serious if the plan is to have AI bots on another celestial body.

If that were to play out, that would mean the demand for building the AI ecosystem would only increase, and even if it were for off-world deployment, it would still disrupt industries and economies on Earth.

AI will take one look at us, and jump on the rockets and get as far away from us as possible.

This is actually a really great point. Practically speaking, the internet "lives" on Earth and the communication latency grows the further away from it you travel.

24 minutes between Earth and Mars isn't horrible (although that is a 48 minute round trip to get an answer) but if people were living in a colony then even the current generation of LLM AIs could significantly improve daily life.