Wow - lots of comment on this issue!I would never check a guitar whose sentimental value exceeded my willingness to risk its loss, as so aptly put above, "guitar accidents do happen" - they also happen on stage, or even in your living room ... but air travel increases the likliehood of accident. That's why I would simply pay the few extra bucks for replacement insurance.
My advice on NOT LOOSENING STRINGS when shipping a guitar came from luthier Matthew Larrivee or Larrivee guitars in Canada. I believe you will find that the instruments strength, and ability to withstand abuse is at its best when the strings are tightend to playing pitch, afterall - that is meant to be its normal state.
If you have doubts, please contact the instrument manufacturer, they can give you the best advice.