I've never flown in the area, but checking it out on Foreflight shows the traffic pattern altitude as being 1100 ft under a 1300 ft floor Class C floor, on the edge of the Class C. Part of the Quonset State control zone extends up into the Class C, and otherwise it'll be Class D.
I imagine a lot of people do enter the area level at 1100 ft, under the Class C, and talk only to the tower. That aside, the requirements for Class C are that you be in contact with ATC and in this instance with the airport control zone extending up into the Class C area, I would assume contact with Quonset State tower would qualify as being in contact with ATC as long as you're simultaneously inside the airport control zone and the Class C.
It's a interesting question, and I'll be interested to see if anybody with local knowledge can clarify.