I happen to be in Sicily now so i can answer most questions..
with the 1E houses, you're looking at about 15K in renovations over 3 to 5 year depending on the one you pick. They tend to also have a few places around the 5K price point that are cheaper in the long run and better equiped.
Internet actually works.. it works... that alone has been worth the move.
I could manage 5k Euro to renovate a place. The lottery aspect of it, not being able to take much of a close look at the places first, that could be problematic. The question of neighbourhood and neighbours.
I saw on some articles that kinda you really only get to pay 1 Euro for the place if no one else is in the running. If other people express interest, it goes to the highest bidder. From that Sambuca document, it looks like auction prices can end up in the thousands of euros
Helluva an idea though. A small, renovated, old house in Italy. Would be cool