Not trying to be rude or smartasseed, but I am genuinely curious, in an emergency situation as this will marinas go round the clock on haulouts or just go home at closing time?
Probably not round the clock.
I know that in some Pensacola, FL marina/yards, you have to pay a few hundred dollars to be on the haul out list before peak storm season. In the event of a hurricane, you must get your boat to the facility within a prescribed time and you will be guaranteed to be hauled out. The fee to be on the list does not include the actual haulout fee nor does it include the daily storage/yard rate. If you don't pay to be on the list, you probably aren't going to get hauled out.
Five years ago, when I purchased my boat and had it off loaded in a yard in New Orleans, there was a minimal Cat 1 storm that was heading to south Louisiana. My boat was already on stands and not rigged yet. The marina did haul quite a few boats two days before the storm. They may have worked overtime a couple hours a day; however, I didn't recall them working round the clock....may not have had the demand to warrant longer hours. They are not going to risk their employees lives, especially if an evacuation of the area is called by local officials. Another factor is available yard space and stands, most yards that I have been in are at least half full, or more, at any given time on the coast. They don't have an unlimited amount of yard space nor stands to haulout and store an unlimited amount of boats.