No, the condition you describe will not damage your firearm. If you do so, there are a few conditions you might consider though. The first, and the obvious one, is safety. While it will not damage your gun to keep a magazine loaded and connected, you must of course keep this gun properly locked away from anyone not fully familiar with it's action and proper safety procedures. The other thing, and although this one is minor and unlikely .. is that if you keep your gun parts heavily oiled, then it might be in your best interest to leave the magazine out for storage, as there is some small possibility of oil damaging the primers and rendering the ammunition unusable if it somehow makes it's way on to the rounds. I've never seen this happen, or known anyone who it has happened to, but I've been told that this is remotely possible.