No, LEOSA does not allow him to carry anywhere. However, in FL, the “no gun” sign does not have the force of law. The sign does however have the force of a property owner’s rights, and if asked to leave due to carrying a gun, he must leave.
“Although LEOSA preempts state and local laws, there are two notable exceptions: “the laws of any State that (1) permit private persons or entities to prohibit or restrict the possession of concealed firearms on their property” (such as a bars, private clubs, amusement parks, etc.), or “(2) prohibit or restrict the possession of firearms on any State or local government property, installation, building, base, or park” “
Thanks for the correction. That’s actually comforting that federal law bothers to respect individual property rights.