Air pockets underwater mean that it is trapped air. This air may not always be of a healthy breathing quality, ask the cave explorers or even cave divers and you might hear unpleasant stories about that, even people dying.
You can never be sure trapped air is safe to breathe unless you analyze it at that moment. It is not only the oxygen content that can be wrong but there can be all kinds of unwanted substances in unhealthy concentrations in that air.
Together with the things Eric said about it it can be a nasty thing to breathe during freediving. Many advise against the use of "spare air" bottles during freediving because of potential dangers but at least that air is clean and has a known oxygen content.
I must admit that the idea sounds very cool, especially if there are many air pockets in swimming distance of each other you could explore a whole cave with, but I think I will skip the experience and live a healthy life tomorrow.
