If it was just a fabrication hall, would the new building still increase hull production rate?
Any properly equipped, staffed and efficiently integrated additional facility for a production line will increase the "production rate" of a production line compared to not having said additional facility.
The fact you're calling it "just a fabrication hall" and thinking in terms of whether it will "still increase hull production rate" is a bit simplistic.
Think about all of the work that goes into producing a nuclear submarine and all of the subcomponents and fabrication and assembly and movement and all of the efficiency gains that can be made with each part of the process.
Like yeah, having an additional fabrication hall that can do a huge chunk of fabrication work for the modules prior to final assembly will definitely help workflow a lot, and if all other things are kept constant it would be very logical that it can help elevate production rate further relative to not having said additional fabrication hall.