I've been very curious about this as well. I stayed at the Hilton Rome Airport and they have a shuttle to downtown Rome, a 45 minute drive which is a 15-20 euro train each way. They didn't have a roster or verify that you're staying with them at all. Interesting for a hotel that is literally colocated with the terminal. If I had a long layover and knew the schedule, I'd be very tempted. But what would I do with my bags?