Well, if they *did* tie him to a complete cannon, and his son is any measure for Turner intelligence, he probably just pulled and pulled at it until he, about two minutes after Will cut his palm, drowned.
Or he might have come up with an escape in the ten years he was underwater. It would be perfectly canon to me for Bootstrap to be alive after the movie, though.

And thanks again for the pretty! *stares at Norrington screencaps* Also, thanks for pointing out all kinds of minute details I never registered, and things I've noticed but never put in words!