No, they wouldn’t. Under the Act of Settlement the throne goes to the Heir of the Body of the Electress Sophia, exclusing Catholics or those married to Catholics. In terms of British peerage law “Heir of the body” means that only natural children count, not adopted ones. If William does die without an heir though, then Harry would indeed be next in line.
What the heck is that?
Descendant.
The Electress Sophia was a person; specifically, she was a granddaughter of King James I. An “heir of the body” would be a blood descendant.