Yes, eyesight can certainly be cured naturally. See http://www.visionsofjoy.org for info on that, and especially check out the page with testimonials for some confirmation that others have done this and succeeded.
A good book to start with is 'Relearning to See' by Thomas Quackenbush.
There's a teacher in NZ, Peter Grunwald, you'll find his info on the links page at Visions of Joy.