Yes, that's a good deal, great airline but you do have to buy an e-Visa (around 20 EUR) to exit the airport (https://www.evisa.gov.tr/en/). You may not have enough time to enjoy the overnight stay (depends when you land and have to leave). I traveled to Istanbul multiple times solo and really enjoyed it, but it is sensory overload and not ideal to experience in a very short stint (especially if you're jetlagged). If you are adventurous and flexible travelwise, and feel comfortable navigating a busy city like NYC then Istanbul is somewhat similar - lots and lots of people, but the public transit is much simpler to navigate and less extensive (taxis are cheap too but you should print out the hotel address and map and give to the driver - they don't know every area like the back of their hand like in London).
Turkish Air is awesome - they treat you well and for a great price - their prices are very hard to match even although they come with the overnighter/long layover which is a negative for many people. I would go with it regardless (unless you can find a cheaper fare on another carrier) - even if you have to overnight, hotels are not expensive and you'll at least arrive in Rome with a good night sleep (hopefully). PM me if you need hotel recommendations (Old City/Sultanahmet is best but it may make more sense to stay closer to the airport).