I checked out the Air Traffic Controllers Procedures Handbook 7110.65, you can find it at faa.gov, and didn't find anything about your airspace question.

I did however find the requirements for entering class C without a transponder or radios. You would have to have a LOA with the facility, a facility directive, or a special agreement with the class C controlling facility. All of this is found under Chapter 7 Section 8 of that book.

There might be more in there about the airspace question, I just didn't have time to research that far into it.