Yes, you can save it, yes, it's live in-game.

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If you disable the BFG, the Sunbeam will....not try to land in the first place. It's not that exciting. Disabling the BFG before receiving the first Sunbeam transmission definitely works, I've heard it works as long as it's disabled before the landing timer starts. After that it reportedly does *not* work and the Sunbeam gets blown up anyway.

Never repairing/building the radio is the easy way to make sure you accomplish this. Waiting til the end to enable the radio seems to significantly mess with the order you receive messages. It took about 2 hours after disabling the BFG and building a radio to get the Sunbeam message and it was after every other possible radio transmission including the random garbled Warper messages except for the final Warper message which I didn't receive by the time I quit.