You are probably correct that a railpass won’t save you any money, but you seem to be confused about rail passes in general. 17 days is not an issue since you don’t intend to take at least one long train on ride every one of the 17 days you are in Italy. A 4 or 5 day flexible- pass and point to point tickets between Rome and Naples should work. For that matter 15 consecutive days would easily work since you would presumably be in Rome and not taking the train on at least one end of your trip.

I prefer to not use a railpass in Italy since tickets are relatively cheap. Many Italian trains require reservations, which can double the price of the ticket and aren’t covered by the rail pass. It’s fast and easy (assuming the kiosks still take non-European credit cards) to buy a ticket with reservation from the kiosks, but you almost always have to wait in line to buy “just a reservation” to use with a rail pass.

Some national rail companies offer discounts for students and youth, but others don’t. Often, youth or student discounts on point to point tickets are only offered to citizens of the particular country. See what you can find at www.trenitalia.com. Unless you have a European issued credit card, you won’t be able to buy tickets on-line from trenitalia so probably can’t take advantage of advance purchase specials. If you’re at a ticket counter, always ask for a student ticket — sometimes you’ll luck out. An ISIC card may have other benefits, but your student ID should work if you ever get asked for proof for travel purposes.