Absolutely, it's included ... although we had seen it the day before on our own, and we ditched the Tauck tour at Sforza Castle. Since we did not finish that tour, I have no first hand knowledge of it, but I believe the Tauck tour does not go inside the building. The lines are long.
The day we saw it on our own was a Monday, and I had read that access to the roof of the Duomo was closed on Monday. But that day it was open - I clearly saw people on the roof. If I had known that, I would have planned the day so that we could have done the roof thing.
The tour is a walk around outside. Going inside is not part of the tour. If you want to go inside you will should investigate whether they give out timed tickets, get a city pass if it exists, or get there very early. Lines are long.
A friend and I flew to Milan on 9/25/19 arriving in Milan on 9/26/19 about 10:00 AM after a short layover in Amsterdam. I purchased the tickets for a guided tour of the Duomo, with a visit to the roof for 9/27/19, as a tour of the inside of the Duomo was not on the Tauck itinerary. (Our tour began on 9/28/19.) We took the elevator up to the roof top as it was included as part of the guided tour. I have some arthritis in my knees, so climbing the stairs was not an option for me. Be advised that there is another elevator that goes down from the roof top to ground level, but comes out at the exit, at the rear of the Duomo. If the rest of your party is exiting via the stairway, it is a slow process going down to the spot that exits inside the Duomo. The stairway exit is not identified in any way inside the church, just a roped off area, so you wouldn't know to look for someone at that location. The stairway has traffic going up and down at the same time and people may need to stop to let others go by them. My friend took the stairs down to the ground floor and we missed connecting with each other when we came out at different locations. If you have some people in your party who will need to use the elevator, it would be advisable to set up a meeting point. We connected again at the tour building where the electronic tour voice box is to be returned. .
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The day we saw it on our own was a Monday, and I had read that access to the roof of the Duomo was closed on Monday. But that day it was open - I clearly saw people on the roof. If I had known that, I would have planned the day so that we could have done the roof thing.
Watch out for the birds!
A friend and I flew to Milan on 9/25/19 arriving in Milan on 9/26/19 about 10:00 AM after a short layover in Amsterdam. I purchased the tickets for a guided tour of the Duomo, with a visit to the roof for 9/27/19, as a tour of the inside of the Duomo was not on the Tauck itinerary. (Our tour began on 9/28/19.) We took the elevator up to the roof top as it was included as part of the guided tour. I have some arthritis in my knees, so climbing the stairs was not an option for me. Be advised that there is another elevator that goes down from the roof top to ground level, but comes out at the exit, at the rear of the Duomo. If the rest of your party is exiting via the stairway, it is a slow process going down to the spot that exits inside the Duomo. The stairway exit is not identified in any way inside the church, just a roped off area, so you wouldn't know to look for someone at that location. The stairway has traffic going up and down at the same time and people may need to stop to let others go by them. My friend took the stairs down to the ground floor and we missed connecting with each other when we came out at different locations. If you have some people in your party who will need to use the elevator, it would be advisable to set up a meeting point. We connected again at the tour building where the electronic tour voice box is to be returned. .
Even using the elevator to go up, it is still necessary to climb some stairs to the very top of the roof area tour.