I was actually thinking of the same thing, so I did a bit of research. I don't think would want to try to carry a standard guitar gig bag on my back while riding. A quick google turned up some backpack-type gig bags on musicians friend and other sites. In riding position, the guitar neck might interfere with your head if you are in drops or anything low. On the other hand, if you are somewhat vertical, it should be fine.

Also, Arkel sells the hook kit for their panniers for $24US right from their website. Enough to mount two bags. Maybe you can connect that into a good quality gig bag. You would need a sheet of plastic to stiffen the bag. I have a Taylor Big Baby that comes w/ a decent bag that I think would hold up well. Heel clearance would be the biggest issue. Also, you could probably rig a guitar of any sort onto a trailer.

If you come up w/ a solution, please post it.