Fallout had lyrics from Burning In The Skies...SOL has lyrics from The Catalyst. So it's unlikely that SOL was a demo of Fallout. Either way, I wouldn't say that either track you've mentioned is a demo of a full length ATS track. To me SOL just seems like an interlude the band had been working on for consideration on the album, before deciding to go a different route.
My theory is that they had a plan for ATS to have an acoustic closer, had a few ideas (SOL among them), and chose The Messenger in the end.