If they could carry, probably.
However, I carry when I go to see my legislator in a public place that does not bar firearms.
I obey the wishes of the owner if the establish does have such notice, but I will not do business with any business that bars carry.  I stopped using First National Bank of Alaska for that reason.  I do not carry in such places, as I obey the law.  
I don't like gun free, criminal safe zones.  Too many people killed and maimed in gun "free", criminal safe zones.