I would NEVER put a guitar in the cargo hold in anything less than a Calton case. I would especially not put it in there in a gig bag. At minimum, a good hard case is a must, but as Giok points out, you MUST immobilize the head. I have heard both sides of the loosening of strings from different luthiers. I fly with a guitar on 4 flights a week. I loosen the strings, but for the reason that my favorite red head (Maryrrf, whom I simply must sing with one day) says. It simply can't hurt.
If you can afford it, get a very good travel case, especially if it is an instrument you love. I often tell the story of my favorite guitar. Although I play Larrivee now, my favorite sounding guitar ever was a Seagull S6 with a Cedar top. It was just one of those that had the right wood, put together on the right day, under the right conditions, by the right luthier. It was plain looking, but when you struck a chord your body just tingled. Great players would pickup this little red beatup instrument, and invariably, when they handed it back to me they would ask where the hell I got it. I usually carried it onboard aircraft with me, but on one occasion United forced me to check it. I had it in a hard case, but somehow they managed to get it caught and busted 7 braces. It has never been the same since. I now use a Calton case on any instrument that I have a relationship with.