For liability reasons, most shops won’t repair them because the integrity of the tire may be compromised. However, I’ve done my own repairs many times in under 15 min using kits from Amazon.
Even with sealant it still needs to be repaired and/or removed. As was said above, many shops won’t even remove the tire due to what the sealant can do to their equipment.
I would skip self-sealing tires (and run flats) and aftermarket tire warranties every time.
No, they cannot the same way you can patch and/or plug a “regular” tire.
If you have not already bought the car and warranty, it sounds like you are in a rush to find out your answer, but anyway you have three choices:
Call Fidelity and ask them (not open on Sunday? not a great warranty then for Roadside Assistance claims);
Have the F&I person actually hand you a contract with terms that shows a punctured tire is fully replaced; or
Make the dealer swap the tires out for what you want as part of the deal or a for a little bit more $ from you.
I have never had a car with run flats or self-sealing tires or anything like it, nor would I now. I have had cars had run flats taken off by the dealer for zero and also some for a few bucks.
Your biggest problem here is having one tire replaced if it is punctured. You should generally not put one new tire on and have three at a different tread depth due to how the car may be affected adversely in handling. In the event of a puncture is Fidelity buying you three new tires as well for those that are not punctured?