Can an F-16 land on an aircraft carrier, at all?
The hook is for emergency use at airports that have Runway Arrestor Systems.  Lots of non-naval fighters have arrestor hooks for that purpose.

Now, there is nothing stopping someone from landing an F-16 or any other fighter on a carrier deck and using its arrestor system, which works the same way.  The main issues are the proficiency required to do it and the ability of the airframe to take it.

A carrier landing isn't really a landing; you more or less descend into the ocean and the deck gets in the way.  So the airplane needs a pilot trained to do that sort of thing, and an airframe that can do it repeatedly, that is, land with a descent rate of >500 fpm, a "hard landing" for a normal airplane, without developing cracks here and there and everywhere after a few dozen times.

No doubt that in theory, you could take a carrier qualified pilot, check him/her out in the F-16, and that pilot could shoot traps onto a deck with the F-16 using the hook (launching it is another matter in the absence of catapult link).  But they wouldn't be able to do a lot of them before the airframe would be toast.