OC Freedom, I think you're going to find that in just about every state, trespass statutes still carry the weight of law whether one has a gun or not. I know plenty of Floridians, Virginians and others who have this idea that "signs don't mean anything to me", but they completely neglect that while signs may not result in a weapons charge, they certainly may result in a trespassing charge. Depending on the state, trespass may not carry a particularly harsh punishment (I think Ohio leaves trespass as a minor misdemeanor, but Virginia treats it as a serious misdemeanor), but it is still considered a crime. In Virginia it can get you a $1000 fine and 12 months in jail.
Since there is absolutely no case law to back it up, the notion that one can be arrested here in Arizona for trespassing while OCing in a private establishment that has a posted sign based only on the fact that the sign serves as notice to enable a trespassing charge is purely hypothetical. It's possibly possible.
Has it ever happened? Not to anyone's knowledge. Here's the way it will most likely go, probably 99.99% of the time: I OC in a private business that is posted; employee informs me of the sign and policy and asks me to secure the weapon or leave; I refuse and the employee calls law enforcement; law enforcement arrives, tells me to leave, and threatens an arrest for trespassing if I refuse; I refuse or act like a fool and get arrested.
Fortunately, everyone can avoid such issues by following these few, simple steps:
1. Respect private property rights and don't bring your gun in a place that is posted or you know doesn't allow firearms.
2. If you ignore their sign/policy to disarm, don't be confrontational when asked to disarm or leave; do one or the other and complain to the owners/corporate.
3. If law enforcement is called without an employee ever contacting you about the issue, refer to step 2.
4. What sign?
With few exceptions due to dire circumstances, step 1 is the best way to do things IMO.