DB has an ICE that runs the route later that morning, Basel Badischer to Basel SBB. If I purchase a normalpreis fare on that train, can that function as my "ticket" for the final portion of the journey? This would give me the rail pass for Hamburg to Basel Badischer, the standard ticket between the Basel stations, and the paid supplement for the entire route. I'd like to avoid the potential drama mentioned above.

Thanks everyone for your input; I appreciate it!