Brief question about Conway’s Game of LIfe and AI

Conway’s Game of Life is Turing-complete. Therefore, it is possible to create an AI in it. If you created a 3^^3 by 3^^3 Life board, setting the initial state at random, presumably somewhere an AI would be created. Would this AI somehow take over the whole game board, if given enough time?

Would this be visible from the top, as it were?

EDIT: I probably meant 3^^^3, sorry. Also, by generating at random, I meant 50% chance on. But any other chance would work too, I suspect.