That's a very interesting idea.
There's more. Snoke is actual a part of the same AI. See, after Luke an his New Jedi order found the main frame, Hux tampered with it trying to destroy it in order to bring the remnants of the Empire to power. He failed and instead caused it to split into two halves, the evil(Snoke) and the good(Rey).
Wouldn't they keep Rey's mainframe on a colder planet? Or is all the water from the melted ice and that's why Luke looks so puzzled when Rey shows up because he thought she was destroyed for sure?
Kylo attacks the MCP
Rey's mainframe is kept there because it was something of a sacred location to the Jedi, so the council erected a temple there to hold it. Rey is actually thousands of years old, but part of her design is to "die" and be reconfigured every 100 or so years, which is why she has no memories of her life previously.