For the most part I would answer this question with a "No".
We do have the ability to add CAD notes to addresses ("cautions" for certain issues), but these things typically include mental health factors and things of that nature. For example, one address in my district always flags due to their hostility towards officers. The dispatcher usually reads it as: "the residents at this address have a history of fighting with the police, and call notes say to dispatch no less than 3 units for all calls". We also might have call notes on an address for mental health issues where we've had issues in the past (we have one old lady who calls us a few times each week to say that her home is being invaded).
Our dispatch system also allows our dispatchers to see previous calls to that address. So, as they dispatch a call of, say, a family disturbance the dispatcher might also say: "Premise history shows that we were out here in December on a call of a shooting". Our dispatchers will also relay information to us if a complainant has stated that they are currently armed. For instance, we may be dispatched to a burglary in progress, and the dispatcher may tell us: "be aware that the complainant says that she is armed with a revolver, and has locked herself in an upstairs bedroom".
I should also mention that here in Colorado your CCW permit will show up if I conduct a clearance on your name/driver's license.
Anyway, other than those types of examples, we really don't save any information concerning the presence of guns in a given household. To be honest, you pretty much have to be crazy, or simply trying to piss off the police, before you get your address flagged in my ghetto! FWIW, I work for a large city department, and my city isn't known for being the most pro-gun (granted, an "anti-gun" city in Colorado is far more pro-gun than a "pro-gun" city in NY or CA).