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No novice diver is going to remain at depth in an out-of-air situation, under any circumstances. The point of training the CESA is to teach people not to hold their breath and hurt themselves when they panic and bolt for the surface. This panic reflex is so strong that it takes dozens of hours of training and practice to be able to signal a buddy and breathe off their air supply in a real emergency situation.

You can see this reality reflected in the rescue diver certification (a fairly advanced level of training), which revolves around how to stop people bolting for the surface when they have trouble getting air. Rescue divers are taught some fairly extreme measures—you pull the person's regulator, yank their fins off, pull off their mask, and hold them down by the tank valve, anything you can do to prevent them surfacing at high speed. Better a briefly unconscious diver than one with an air embolism.