No. To visit the Dome of St. Peter an extra ticket is required to be done directly on site. It costs 6 euro if you want to climb all 551 steps, while it costs 8, you intend to use the lift to the terrace and then continue on foot. None of our tours include going up to the Dome. On Sunday and Wednesday the Dome of St. Peter is closed to the public, it is possible to visit it on all other days.