I spoke to some of the biologists with the Florida Fish And Game Commission including "Woody" Woodward and Blair Hamman. It was indicated that there is research to support small alligators surviving in saltwater for at least six days. It would thought larger individuals might be able to persist longer.
http://tinyurl.com/28xnqt8
I asked what they would advise if someone came across a submerged alligator in the ocean. As common sense would support, to not approach too closely, startle or threaten the alligator. They can sprint at around 8 to 10 mph on the surface, likely doing something less than that underwater. In any event, faster than we can swim. Mr. Woodward indicated that an alligator might cover 10 to 15 miles fairly easily in a day. He indicated that in clear water, alligators may sometimes hunt by remaining motionless on the bottom. They stay that way in the fashion of stonefish until prey comes close enough to strike. Looks like the alligator in the photo might have been contemplating something like that? Who knows.
Someone should pass that possibility on to Laz. Not sure there will be a next time but if there is, even more distance might be a good idea. May ruin a good photo op but beats ruining a perfectly good diver. Alligators aren't all that able to chew prey into smaller bits. They use rotational forces in a "death roll" to drown and then dismember prey. Some prey is stashed underwater following this to soften up, like hanging meat only submerged. So, they seem to do ok dealing with prey underwater. More at:
Crocodilians in the US: The American Alligator and The American Crocodile- Final Draft
Clip of a small gator rolling to manage a frog for dinner:
YouTube - alligator death roll