If the board is big enough, I don't know that it matters what the chance of any given cell starting alive or dead is.
What matters isn't just what the local configuration looks like but how well it can expand. Expanding into empty space is easy. Expanding into densely populated space is much tougher.
Re the radar idea. Radar in some sense (and most real world senses for that matter) work because they give information much faster than the environment moves. in the case of real life radar, or vision, this is as fast as the laws of physics allow. Unfortunately, in Life, the equivalent speed of light is not a speed at which stable objects can self-propagate. Objects can only propagate in life at most c/2. Worse, some very simple configurations meet this speed. This means that if one runs into a bad configuration one will likely get that data the same time that the disruptive c/2 stuff is coming in. Configurations that can move themselves and leave trails will move much slower than c/2 and only send back messenger gliders every few moves. Finally, even if one did get data back, since most complicated configuration are only barely stable, it is unlikely one could get any information other than that something occurred at around a specific area that disrupted your configuration.
I disagree with your final point, that it is unlikely that it would be possible to get information other than "something occurred at around a specific area;" however I agree with your other points.
A detailed computer is likely to be very unstable. Even if it could collect lots of information about the environment reliably at a distance, it would not be able to retrieve or utilize that information quickly.
In a large enough board, however, we would expect to see a computer that was essentially isolated except for a few small stable patterns which ...
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.