I believe that if the apartment complex has an issue with it and confronts someone about it, they will lose, even if it was in the rental agreement. It's an unconscionable clause, meaning there is unfair bargaining going on. Basically contracting law is an even trade with a little wiggle room. If you provide something, they have to provide something back in a mostly equal way. Similarly, if you give something up, they have to provide something reasonably close to what you surrendered. In this example, they take away your ability to have a firearm. In order for it to be equal, the management would have to provide something like 24/7 armed security and provide a written guarantee that they will patrol your specific apartment for security purposes. Of course, they're not going to do that. But the example still holds: If you're giving up your right to have a firearm on you, what are they providing to fill that void to an equal level. If they are just summarily dismissing your right without an equal balance, that clause is unconscionable and therefore, unenforceable.
State firearms laws also state that regardless of any contract or otherwise you have the right to firearms inside your residence. The complex would try to argue that their sign prohibits carrying on the grounds. There you have a problem... You are leasing property on the premises, you must be allowed reasonable access to enjoy your leased structure. The complex (in court anyway) would have to concede that you have the right to carry within the apartment and in your car, the parking lot, etc. Therefore, you must be allowed reasonable access to your apartment between there and the parking lot. Short version: Screw the sign.
As someone stated earlier, the sign is probably meant for people that don't belong there whether or not they intended to restrict the people that actually live there. The sign allows police to arrest someone for trespassing easier if they don't belong. But as someone else had said -- the fact that the no firearms sign was attached -- might want to find somewhere else to live. People don't put signs up to actually prevent something, most people put signs up because something happened and they want to prevent it from becoming an on-going event.