Early AM flight out of Naples?

It could be very realistic if there was a flight out of Naples to the US at 6 am. But there are no flights to the US from Naples and the first flight out of Naples anywhere is actually not a 6am but at 6:15 (to Munich, Germany). If that is the one you intend to take, then yes, it is very realistic. Just get up on time to be at the airport about one hour prior to departure.

Adding to Roberto's reply, whether it's realistic or not has nothing to do with your 2 weeks prior to departure, but everything to do with where you will be on your last night. If you are in Naples, and can get up early enough, it's fine. If you are somewhere else (say, Sorrento), you will have to book a car (very expensive) and get up VERY early. I wouldn't do this, but some would.

Flying out of smaller European airports to the gateway cities (to the U.S.) does appear to often require 6:00 a.m. flights. I prefer to take outgoing flights that are closer to 11:00 or later. That means scheduling my last day/night staying in larger cities with direct U.S. flights. In this case, Naples is just about 2 hrs. by train from Rome. Anytime I have to get up at 3:00 or 4:00 to fly out, there's little sleep from the night before. It's hard enough getting back to the U.S. tired from the flight. But when you start with little or no sleep, it's almost painful when arriving home.

Unless you are on a flight from Rome FCO straight to the US on Alitalia/Delta (JFK, ATL), UsAir (PHL) or United (IAD), if you have to go through another EU hub first you still need to leave very early from Rome. Also the aforementioned flights direct to the US leave at around 10, and since they are not Schengen area flights, you need to be at FCO airport by 7 or 7:30am. The only one that leaves later (after 11am) is the USAir to PHL. Taking the train back to Rome from Naples the morning of the flight is not really an option. One would still need to spend the night before the flight in Rome. At that point, one might as well leave Sorrento and find a hotel next to the NAP airport the night before the flight, rather than back tracking all the way to Rome.