I thought about this too, but I think it would be risky... you risk damaging the guitar and maybe the bike... plus you risk the guitar hitting you in an accident too. At least that's what I concluded when I thought about this.
If you want to carry a guitar on your bike and you don't want to risk an old favorite Martin Made an Acoustic for just such shenanigans a few years back called the Backpacker.It is an odd looking little thing but will surprise you with it's sound.It is still in production and still cheap,It ain't no D28 or 35,but for riding and camping it is handy, http://www.sweetwater.com/store/detail/BackPackerS/
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