It depends on where you are. Some states require notification, some do not. That's the first determiner.
I live in Kalifornia (notification not required). Gun's are not PC. Most cops I'm sure would be OK with a CCW but some will not be. I would never notify in Los Angeles. The Cops have an average time in the job of less than 5 years. The Chief hates citizens having guns. If I were in one of the counties known to be gun friendly I might notify but not to a young cop. I've heard too many stories on cops who want to take possession of the gun, unload it, and who have no familiarity with guns other than the one they carry.