During a disaster such as a major hurricane, can this law give the police the legal authority to restrict guns from a broad class of citizens?
Doubt it.
Florida Statutes 790.01(3) (a) which provides that you may now carry a concealed weapon or firearm on or about your person during a mandatory evacuation while in the act of evacuating. No CWL is required however, the weapon or firearm must be kept concealed
There is also another law (signed by Jeb, can't find the statute right now) that says cops can't confiscate firearms if you're evacuating or hunkering down with your firearms(Like what happened in New Orleans during Katrina).Just don't walk around with them uncased except on your own property.