The signs don't mean squat in Florida. However, that isn't the point. Yes, concealed is concealed and I can still carry there if I want. Doesn't matter. If a business posts signs prohibiting legal firearms, I refuse to do business with them. I don't care if they are the bestest, cheapest, mostest store in the hemisphere, I refuse to spend my money there.
If enough people would likewise boycott these stores, there would be an effect. The local Blockbusters posted no CCW signs a few years ago. It only took a few weeks of boycotting them for the signs to vanish.